Yes, there are scriptures which prescribe using the mantra 'Gananam Tva Ganapatim.. ' to worship Lord Ganesha. Let's look at some scriptural references:
1) Sage Vyasa says so in Padma Purana:
In the Shristikhanda of the Padma Purana chapter 65, sage Vyasa specifies to use this mantra to worship Lord Ganesha:
व्यास उवाच-
नांदीमुखेषु सर्वेषु पूजयेद्यो गणाधिपम्|
तस्य सर्वो भवेद्वश्यः पुण्यं भवति चाक्षयम्||
गणानां त्वेति मंत्रेण सर्वयज्ञघटेषु च|
सर्वसिद्धिमवाप्नोति स्वर्गं मोक्षं लभेन्नरः||
मृण्मये प्रतिमायां च चित्रे चाथ दृषण्मये|
द्वारदारुणि पात्रे च हेरंबं लेखयेद्बुधः||
अन्यस्मिन्नपि देशे तु सततं दृष्टिगोचरे|
स्थापयित्वा तु हेरंबं शक्त्या यः पूजयेद्बुधः||
तस्य कार्याणि सिद्ध्यंति दयितानि समंततः|
न विघ्नं जायते किंचित्त्रैलोक्यं वशमानयेत्||
विद्यार्थी लभते विद्यां वेदशास्त्रसमुद्भवाम्|
अन्यां च शिल्पिविद्यां च विजयां स्वर्गदायिनीम्||
धनार्थी विपुलं वित्तं कन्यां साध्वीं मनोरमाम्|
ऐश्वर्यं धर्मसाध्यं च तनयं कुलमोक्षदम्||
Vyasa said:
He, who would worship the lord of the Ganas in the
Nandimukha, has everyone under his control, and his merit
becomes inexhaustible. A man obtains all (kinds of) prosperity in all sacrifices by means of (the recital of) the hymns 'Gananam tva' and
would obtain heaven and salvation. A wise man should draw the figure of Ganesha on a clay idol, or in a picture (carved out) of stone or on the wood of the door, or in a pot. A wise man, who, after having installed the idol of
Ganesha, even in any other place which would always be visible,
would worship Ganesha according to his capacity, fully gets his
desired objects fulfilled. He has no difficulty and he would
bring the three worlds under his control.A student obtains knowledge from the Vedas and sacredtexts, and also other knowledge (like that) of the fine arts,
which is successful and which would give (i.e. lead) him (to)
heaven
Thus, as clear from the above passage, Sage Vyasa is recommending to worship Lord Ganesha using the mantra 'Gananam Tva'.
2) Lord Kartikeya says so in Shiva Purana:
Lord Kartikeya in Kailasha Samhita chapter 13 of Shiva Purana describes procedure to perform worship of Lord Shiva. While telling such he mentions to use the mantra 'Gananam Tva' to worship Lord Ganesha:
।। सुब्रह्मण्य उवाच ।।
अथ मध्याह्नसमये स्नात्वा नियतमानसः ।।
गन्धपुष्पाक्षतादीनि पूजाद्रव्याण्युपाहरेत।।।।
नैर्ऋत्ये पूजयेद्देवं विघ्रेशं देवपूजितम्।।
गणानां त्वेति मन्त्रेणावाहयेत्सुविधानतः ।।२।।
रक्तवर्णं महाकायं सर्व्वाभरणभूषितम्।।
पाशांकुशाक्षाभीष्टञ्च दधानं करपंकजैः ।। ३ ।।
एवमावाह्य सन्ध्याय शंभुपुत्रं गजाननम्।।
अभ्यर्च्य पायसापूपनालिकेरगुडादिभिः ।।४।।
नैवेद्यमुत्तमं दद्यात्ताम्बूलादिमथापरम्।।
परितोष्य नमस्कृत्य निर्विघ्नम्प्रार्थयेत्ततः ।। ५ ।।
औपासनाग्नौ कर्त्तव्यं स्वगृह्योक्तविधानतः ।।
आज्यभागान्तमाग्नेयं मखतन्त्रमतः परम् ।। ६ ।।
Subrahmanya said:-- Then at midday he shall take bath. With the mind fully controlled he shall
gather materials for worship such as fragrant flowers, Aksatas etc. With the mantra, "Gananam tva" he shall as enjoined invoke lord Ganapati
worshipped by the gods. He shall worship him in the south-west. After invoking the elephant-faced lord Ganapati son of Siva, of red colour,
huge body, bedecked in ornaments and holding noose, goad, Rudraksa and boon in his
lotus-hand he shall worship him at dusk. He shall offer milk pudding (sweet pie),
coconut jaggery and other things as Naivedya and also the leaf. After propitiating
and bowing to him he shall pray for warding off evil. Thereafter the rites of sacrifice concluding with the sharing of clarified
butter shall be performed in the Aupasana fire according to the rules of one's Grhyasutra.
Thus here, Lord Kartikeya is himself referring to worship Lord Ganesha using 'Gananam Tva' mantra.
3) Lord Shiva himself says so in Shiva Purana:
Lord Shiva in the chapter 7 of Kailasha Samhita of Shiva Purana states:
प्रणवं गुं गुरुभ्योन्ते नमः प्रोच्यापि देशिकम् ।।
समावाह्य ततो ध्यायेद्दक्षिणाभिमुखं स्थितम् ।। १२ ।।
सुप्रसन्नमुखं सौम्यं शुद्धस्फटिकनिर्मलम् ।।
वरदाभयहस्तं च द्विनेत्रं शिवविग्रहम् ।। १३ ।।
एवं ध्यात्वा यजेद्गन्धपुष्पादिभिरनुक्रमात् ।।
पद्मस्य नैर्ऋते पद्मे गणपत्यासनोपरि ।।१४।।
मूर्तिम्प्रकल्प्य तत्रैव गणानां त्वेति मंत्रतः ।।
समावाह्य ततो देवं ध्यायेदेका ग्रमानसः ।। १५ ।।
रक्तवर्णं महाकायं सर्वाभरणभूषितम् ।।
पाशांकुशेष्टदशनान्दधानङ्करपङ्कजैः ।। १६ ।।
गजाननम्प्रभुं सर्वविघ्नौघघ्नमुपासितुः ।।
एवन्ध्यात्वा यजेद्गन्धपुष्पाद्यैरुपचारकैः ।। १७ ।।
कदलीनारिकेलाम्रफललड्डुकपूर्वकम् ।।
नैवेद्यं च समर्प्याथ नमस्कुर्याद्गजाननम् ।।१८।।
पद्मस्य वायुदिक्पद्मे संकल्प्य स्कान्दमासनम् ।।
स्कन्दमूर्तिम्प्रकल्प्याथ स्कन्दमावाहयेद्बुधः।।१९।।
उच्चार्य्य स्कन्दगायत्रीं ध्यायेदथ कुमारकम्।।
उद्यदादित्यसंकाशं मयूरवरवाहनम्।।6.7.२०।।
After saying "Om gum gurubhyah namah" he shall invoke the preceptor and
meditate on him as seated facing the south, with a delightful face, looking gentle
and crystal pure, showing the mystic gestures of boons and protection with his
hands in the form and features of Siva but with two eyes. After meditating thus he shall worship Ganapati with scents, flowers etc. in
the proper order assigning him a scat on the lotus to the south-west of the
mystical diagram with the mantra "Gananantva" etc. After invoking the lord he
shall meditate on him with concentration. He shall be conceived as red in complexion with a huge body bedecked in
ornaments holding a noose, a goad, boons and teeth, with elephantine face
destroying the hindrances and obstacles of his devotees. After meditating thus he
shall worship him with scents, flowers and other services. After offering him the
Naivedya of plantain fruits, coconuts, mango fruits and sweet balls he shall make
obeisance to the god. In the lotus to the north-west of the diagram the devotee shall conceive the
form of Skanda and invoke him too. Repeating Skandagayatri he shall meditate on Kumara shining as the rising
sun, seated on the peacock, with four arms and splendid limbs, bedecked in coronet
holding mystic signs of boons and protection, a spear and a cock as well.
Thus here, Lord Shiva himself is telling to invoke Lord Kartikeya using Skandha Gayatri and to invoke Lord Ganesha using 'Gananam Tva' mantra.
4) Ganesha Sahasranama of Ganesha Purana:
Ganesha Purana contains Ganesha Sahasranama which was recited by Lord Shiva to invoke Lord MahaGanadhipati during Tripura Samhara incident. Verse 9 of Ganesha Sahasranama states:
कविः कवीनामृषभो ब्रह्मण्यो ब्रह्मणस्पतिः ॥
ज्येष्ठराजो निधिपतिर्निधिप्रियपतिप्रियः ।
kaviḥ kavīnāmṛṣabho brahmaṇyo brahmaṇaspatiḥ ॥
jyeṣṭharājo nidhipatirnidhipriyapatipriyaḥ ।
Kavi (One who is poet or in the form of poetry), Kavinamrsava (Greatest of the poet), Brahmanyo (who loves Vedas), Brahmanaspati (who is the Lord of Creator), Jyestharaja (Who is the eldest), Nidhipati (Who is the Lord of treasures), Nidhipriyapatipriya (who is loved by Kubera/ Nidhipati)
As we can see the use of words 'Kavi Kavinam', 'Brahmanyo Brahmanaspati', 'Jyestharaja' etc.. in the single verse, it is clear that this is the same Rigvedic verse of 'Gananam tva' and other related mantras.
5) Brahmanaspati in AtharvaVeda:
While commenting the above name 'Brahmanaspati' of the Ganesha Sahasranama, Bhaskaraya quotes the vedic wisdom "vAgvai brahma patis tasyA itesya brahmanaspati" which means "Vag (Speech) is Brahman and Lord of it is Brahmanaspati". We can find various attributes of Lord Ganesha in the form of Brahmanaspati as well. If we have to say the three main attributes/forms of Ganesha we will immediately remember his Ekadanta, Vakratunda and Obstacle removing power. Ganesha is also called by the name Danti in the Vedas.
AtharvaVeda too prays Lord Brahmanaspati for making Dantas (teeth) as Shiva:
तौ दन्तं ब्रह्मणस्पते शिवौ कृणु जातवेदः ॥१॥ (६,१४०.१ )
tau dantaM brahmaNaspate shivau kRRiNu jAtavedaH
Oh Brhamanaspati make these Dantas (teeth), Shiva (auspicious) with your power (Jataveda)
AtharvaVeda prays Lord Brahamanaspati to cure disease which made them Vakra-Mukha:
अयं यो वक्रो विपरुर्व्यङ्गो मुखानि वक्रा वृजिना कृणोषि ।
तानि त्वं ब्रह्मणस्पते इषीकामिव सं नमः ॥(७,५६.४ )
ayaM yo vakro viparurvya~Ngo mukhAni vakrA vRRijinA kRRiNoShi |
tAni tvaM brahmaNaspate iShIkAmiva saM namaH ||(7,56.4 )
Oh Lord Brahmanaspati please cure my damaged Vakra mukha (twisted face) and twisted jaw.
AtharvaVeda prays Indra as Lord Brahmanaspati to remove obstacles and make the path Shiva (auspicious):
इमा या ब्रह्मणस्पते विषुचीर्वात ईरते ।
सध्रीचीरिन्द्र ताः कृत्वा मह्यं शिवतमास्कृधि ॥६॥ (१९,८.६ )
imA yA brahmaNaspate viShuchIrvAta Irate |
sadhrIchIrindra tAH kRRitvA mahyaM shivatamAskRRidhi ||6|| (19,8.6 )
Oh Lord Brahamanaspati Indra, those directions like east where Vayu runs as hurricanes, please make it run in appropriate way and make our path Shiva (auspicious)
Thus, as we see from mantras above Lord Brahamaspati also has attributes related to Danti, Vakra mukha, Shivatamaskrdhi like Lord Ganesha who has similar attributes like Ekadanta/Danti, Vakra tunda, Vighnaharta, etc...
6) Brihaspati and Brahmanaspati:
Brihadaranyaka Upanishad (1.13) makes a subtle difference between Brihaspati and Brahmanaspati. The aspect of Speech (Vak) when it is 'Brihati' it is called as Brihaspati, whereas the aspect of Speech (Vak) when it is 'Brahman' it is called as Brahmanaspati. As both are related to speech, Brihaspati is also sometimes referred to as Brahamanaspati:
एष उ एव बृहस्पतिः; वाग्वै बृहती, तस्या एष पतिः, तस्मादु बृहस्पतिः ॥ २० ॥
एष उ एव ब्रह्मणस्पतिः; वाग्वै ब्रह्म, तस्या एष पतिः, तस्मादु ब्रह्मणस्पतिः ॥ २१ ॥
This alone is Brihaspati, Vag (Speech) is Brihati and lord of it is called Brihaspati. This alone is Brahmanaspati, Vag (Speech) is Brahman and lord of it is called Brhamanaspati.
Bhaskaraya in his Ganesha Sahasranama Bhasya (Khadyota) cites this same verse "वाग्वै ब्रह्म, तस्या एष पतिः, तस्मादु ब्रह्मणस्पतिः" to explain the meaning of Brahamanaspati. Even in the Rigveda 2.23 the devatas Brahmanaspati and Brihaspati are mentioned seperately. Brahmanaspati is the devata of the verses 1, 5, 9, 11, 17, 19. Whereas Brihaspati is the devata of the rest of the verses (2, 3, 4, 6, 7, 8, 9, 10, 12-16, 18).
7) Conclusion:
Skandha Purana also while mentioning the benefits of various Vedic mantras, it lists benefit of 'Gananam tva' mantra as mantra which provides riches with elephants:
If a man for the sake of vehicles performs the Japa of the Rathantaram Saman
there, he obtains splendid and swift vehicles. O excellent Brahmanas, if a devotee who seeks elephants repeats the Mantra
gananam etc. there, that man obtains elephants that flood the ground with their rich. If a man repeats the Mantra na tadraksa etc. for the sake of security, he will obtain it from everywhere when chances are favourable or adverse. (Prabhasha Khanda chapter 36)
Thus as seen from above, Vyasa in Padma Purana, Lord Shiva and Lord Kartikeya in Shiva Purana are recommending to use the mantra 'Gananam tva' to worship Lord Ganesha. The Upabrahmanam of the mantra is also found in Ganesha Sahasranama. So, it is not out of thin air people worship Lord Ganesha with this mantra. Thus one can definitely invoke Lord Ganapati using the mantra 'Gananam Tva Ganapatim':
गणानां त्वा गणपतिं हवामहे
कविं कवीनामुपमश्रवस्तमम् ।
ज्येष्ठराजं ब्रह्मणां ब्रह्मणस्पत
आ नः शृण्वन्नूतिभिः सीद सादनम् ॥
Among the Ganas, to You Who are the Ganapati, we Offer our Sacrificial Oblations, You are the Wisdom of the Wise and Uppermost in Glory, You are the foremost King of the Prayers, presiding as the Brahmanaspati, Please come to us by Listening to our Invocation and be Present in the Seat of this Sacred Sacrificial Altar. (RigVeda 2.23.1)
