Yes, Mata Saraswati is also the Prana Shakti.
The Krishna Yajur Veda (Taittiriya Samhita), says as follows.:
iii. 1. 10. a. May I be pleasing to speech; pleasing to the lord of speech, O divine speech. The sweetness of speech place in me; hail to Sarasvati.
The Sarada Tilaka of 8th century CE, says as follows.:
May the goddess of speech enable us to attain all possible eloquence,
she who wears on her locks a young moon,
who shines with exquisite lustre,
who sits reclined on a white lotus,
and from the crimson cusp of whose hands pours,
radiance on the implements of writing, and books produced by her favour.
– On Saraswati, Sarada Tilaka.
According to Devi / Vak (Speech) Shuktam of Rig Veda.:
अ॒हं राष्ट्री᳚ सं॒गम॑नी॒ वसू᳚नां चिकि॒तुषी᳚ प्रथ॒मा य॒ज्ञिया᳚नाम् ।
तां मा᳚ दे॒वा व्य॑दधुः पुरु॒त्रा भूरि॑स्थात्रां॒ भूर्या᳚ वे॒शयन्᳚तीम् ॥ ३॥
3. I am the Queen of the Universe; I give wealth to those who worship me. I am the all-knowing one and the prime one among the worshippable deities. I enter many bodies as the Atma, taking various forms and with different manifestations, in various ways. Hence, the Devas have incorporated me in various places.
मया॒ सोऽअन्न॑मत्ति॒ यो वि॒पश्य॑ति॒ यः प्राणि॑ति॒ य ईं᳚ शृ॒णोत्यु॒क्तम् ।
अ॒म॒न्तवो॒मान्त उप॑क्षियन्ति श्रु॒धिश्रु॑त श्रद्धि॒वं ते᳚ वदामि ॥ ४॥
4. That one who eats food, who sees, breathes, and hears whatever is said, he does all that only through me (my powers). Those who do not understand me, die. O dear one ! (to the worshipper or devotee), hear this singing of mine with concentration.
अ॒हमे॒व वात॑ऽइव॒ प्रवा᳚म्या॒रभ॑माणा॒ भुव॑नानि॒ विश्वा᳚ ।
प॒रो दि॒वा प॒रए॒ना पृ॑थि॒व्यै ताव॑ती महि॒ना सम्ब॑भूव ॥ ८॥
8. I verily myself breathe forth like the wind, issuing out form to all the created worlds; beyond the heaven, beyond the world (I Exist eternally - beyond space & time) - so vast am I in my greatness.
According to vedic and Sanskrit scholar Shri Kapali Sashtri.:
Here in the case of Devi Sukta, the seer's realization of identity with the Supreme VAk, the creative word- which in the language of Tantra is ParAshakti- may account for the identity of the name (VAk as applied to the RishikA as well as to the DevatA).
It will be more correct to say that the female energy of the Supreme Godhead, ParAdevatA, realizing herself in or choosing the embodiment of VAk Ambhrini, utters the word, the Mantra.
From the "Complete works of KapAli ShAstry".
I hope this clarifies your queries.