Yes. The original Rāmāyaṇa by Mahaṛṣi Vālmīki is indeed said to be śatakoṭi-pravistaram i.e., extending to a 100 crore ślokas.
This is stated in the Matsya Mahā-Purāṇa
अष्टादश पुराणानि कृत्वा सत्यवतीसुतः ॥ भारताख्यानमखिलं चक्रे
तदुपबृंहितम् । लक्षेणैकेन यत्प्रोक्तं वेदार्थपरिबृंहितम् ॥६९॥
वाल्मीकिना तु यत्प्रोक्तं रामोपाख्यानमुत्तमम् ।
ब्रह्मणाभिहितं
यच्च शतकोटिप्रविस्तरम् ॥७०॥ आहृत्य नारदायैवं तेन वाल्मीकये पुनः ।
वाल्मीकिना च लोकेषु धर्मकामार्थसाधनम् । एवं सपादाः पञ्चैते लक्षा
मत्ये प्रकोतिताः ॥७१॥
- 69, 70, 71. The great sage Vyasa, after compiling the 18 Purāṇas, indulged in the composition of the story of Mahābhārata, in order to
magnify their bulk, which was an addition to the Purāṇas, by another
lakhs of ślokas. And in which he has condensed the sense of the
Vedas. The glorious story of Rāmāyaṇa, sung by the sage Vālmīki, at
the instance of Brahmā, also extends to a hundred crore of ślokas.
Brahmā narrated the original Rāmāyaṇa to Nārada Muni; the latter
revealed it to Vālmīki, who gave it to the world, and which is a means
of giving Dharma, Kāma, and Artha. And hence, the total number of
verses in all the Purāṇas and Itihāsas is thus known to be
525,000 in counting.”
English Translation by B.D. Basu
Access the Sanskrit + Hindi translation by the Gita Press Gorakhpur from here
However, the Matsya Purāṇa does not answer any further queries in regards to the OP's questions ( viz. "Does this true original also contain 6 or 7 Kāṇḍas like the one available to us on the Bhūloka? Is Uttara-Kāṇḍa also a part of it?")
For these questions, we may gain some insight from the Ānanda Rāmāyaṇa
भारतं त्विहासञ्च रामायणसमुद्भवम् । यद्वेद्पाठपुण्यं तज्ज्ञेयं
रामायणस्य च ॥६0॥ पाठात्तदर्द श्रवणे व्याख्यातुश्च दशाधिकम् ।
वाल्मीकिना कृतं यत्र शतकोटिप्रविस्तरम् ॥६१॥ तत्सर्वेषामादिभूतं
महामंगलकारकम् । रामायणादेव नाना संति रामायणानि हि ॥६२॥ शेषभूतं
चतुर्विशत्सहस्रं प्रथमं स्मृतम् । तथा च योगवासिष्ठमध्यात्माख्यं
तथास्मृतम् ॥६३॥ वायुपुत्रकृतं चापि नारदोक्तं तथा पुनः । लघुरामायणं चैव
वृहद्रामायण तथा ॥६४॥ अगस्त्युक्तं महाश्रेष्ठं साररामायणं तथा ।
देहरामायणं चापि वृतरामायणं पुनः ॥६५॥ जमरामायणं रम्यं भारद्वाजं तथैव च
। शिवरामायणं क्रौंच भारतस्य च जैमिनेः ॥६६॥ आत्मधर्म
श्वेतकेतुॠषेश्श्चैव जटायुषः ॥६७॥ रवेः पुलस्तेदॆव्याश्च गुह्यकं मंगलं
तथा । गाधिजं च सुतीक्ष्णं च सुग्रीवं च विभीषणम् ॥६८॥
तथाऽऽनंदरामायणमेतन्मंगलकारकम् । एवं सहस्रशः संति श्रीरामचरितानि हि
॥६९। कः समर्थोऽस्ति तेषां हि संख्या वक्त सविस्तरात्॥ शतकोटिनितादेव
विभक्तानि पृथक् पृथक् ॥७०॥
- The piety-merit gained from reading the Vedas and that reading the Rāmāyaṇa is equivalent. Reading the basic text gives half the merit while reading it with expositions gives merit ten times more.
- The Orginal Rāmāyaṇa consisting of 100 crores ślokas composed by the sage Vālmīki is the primordial root of all the known/unknown
Rāmāyaṇas, and is extremely auspicious.
- From a small part of the appendix-endings of that Original 100 crore ślokas Rāmāyaṇa, all the presently known Rāmāyaṇas are
composed viz. the popular '24000 ślokas Vālmīki-Rāmāyaṇa', the
'Yoga-Vāsiṣtha', 'Adhyātma-Rāmāyaṇa', 'the Rāmāyaṇa by Vāyūputra
Hanumāna', 'Nārada-Rāmāyaṇa', 'Laghu-Rāmāyaṇa', 'Brihad-Rāmāyaṇa',
'Sage Agastya authored Sāra-Rāmāyaṇa', 'Deha-Rāmāyaṇa',
'Vrata-Rāmāyaṇa', 'Bhārdvāja-Rāmāyaṇa', 'Śiva-Rāmāyaṇa',
'Kraunca-Rāmāyaṇa', 'Bharata-Rāmāyaṇa', 'Jaimini-Rāmāyaṇa', and
several other Rāmāyaṇas including the 'Rāmāyaṇa by Ātma-dharma', the
Rāmāyaṇa by Jaṭāyu', the the Rāmāyaṇa by Śvetaketu ṛṣi, the Rāmāyaṇa
by Pulastya ṛṣi, the Rāmāyaṇa by Devī, the Rāmāyaṇa by Viśvāmitra, the
Rāmāyaṇa by Sutikṣṇa, the Rāmāyaṇa by Sugriva, the Rāmāyaṇa by
Vibhīṣaṇa, and this meritorious Ānanda-Rāmāyaṇa.
- In this way thousands
of Rāmāyaṇas have been composed which sings the glories of Rāma and
his character.
- There is none capable enough to elucidate on each and every Rāmāyaṇa. But know that, the Original Rāmāyaṇa which consists of 100
crores of ślokas is the source of all these Rāmāyaṇas.
To Conclude:
So, it is clear that the Original Rāmāyaṇa by Mahaṛṣi Vālmīki is the source of all the Rāmāyaṇas including the '24000 ślokas Vālmīki-Rāmāyaṇa'.
The scriptural information about the division of this 'True Original Rāmāyaṇa' also containing 6 or 7 Kāṇḍas like the one available to us on the Bhūloka is not mentioned. We cannot comment on the structure of the Original, from the information available.