Yes, Ramanujacharya quotes from Baudhayana's Vritti several times.. First of all, in this section his commentary on Adhyaya 1 Pada 1 Sutra 1 of the Brahma Sutras, Ramanujacharya gives two quotes from Baudhayana:
The purport of the entire Sûtra then is as follows: 'Since the fruit of works known through the earlier part of the Mîmâmsâ is limited and non-permanent, and since the fruit of the knowledge of Brahman--which knowledge is to be reached through the latter part of the Mîmâmsâ--is unlimited and permanent; for this reason Brahman is to be known, after the knowledge of works has previously taken place.'--The same meaning is expressed by the Vrittikâra when saying 'after the comprehension of works has taken place there follows the enquiry into Brahman.' And that the enquiry into works and that into Brahman constitute one body of doctrine, he (the Vrittikâra) will declare later on 'this Sârîraka-doctrine is connected with Gaimini's doctrine as contained in sixteen adhyâyas; this proves the two to constitute one body of doctrine.'
I discuss this subject in my answer here. In any case, another instance of this is in Ramanujacharya's commentary on Adhyaya 1 Pada Sutra 10, where he says this:
Up to the time of final release there arise in the soul invested by name and form the cognitions of objects different from itself. During deep sleep the souls divest themselves of names and forms, and are embraced by the 'Sat' only; but in the waking state they again invest themselves with names and forms, and thus bear corresponding distinctive names and forms. This, other scriptural texts also distinctly declare, 'When a man lying in deep sleep sees no dream whatever, he becomes one with that prâna alone;--from that Self the prânas proceed, each towards its place' (Kau.Up. 111,3); 'Whatever these creatures are here, whether a lion or a wolf or a boar or a gnat or a mosquito, that they become again' (Kh. Up. VI, 9, 3).--Hence the term 'Sat' denotes the highest Brahman, the all-knowing highest Lord, the highest Person. Thus the Vrittikâra also says, 'Then he becomes united with the Sat--this is proved by (all creatures) entering into it and coming back out of it.' And Scripture also says, 'Embraced by the intelligent Self.'
Then in his commentary on Adhyaya 1 Pada 3 Sutra 7, Ramanujacharya says this:
Now in the text under discussion instruction is given about a being called 'the True,' and possessing the attribute of 'bhûman,' as being something additional to the individual soul; and this being called 'the True' is none other than the highest Brahman. Just as in the series of beings beginning with name and ending with breath, each successive being is mentioned in addition to the preceding one--wherefrom we conclude that it is something really different from what precedes; so that being also which is called 'the True,' and which is mentioned in addition to the individual Self called Prâna, is something different from the individual Self, and this being called 'the True' is the same as the Bhûman; in other words, the text teaches that the Bhûman is the highest Brahman called 'the True.' This the Vrittikâra also declares: 'But the Bhûman only. The Bhûman is Brahman, because in the series beginning with name instruction is given about it subsequently to the individual Self.'
Finally in his commentary on Adhyaya 1 Pada 1 Sutra 31, Ramanujacharyas says this:
From the fact that the text, 'And indeed to him who thus knows the Brahma-upanishad. the sun does not rise and does not set; for him there is day once and for all,' calls the whole Madhuvidyâ a 'Brahma'--upanishad, and that the reward declared is the attainment of Vasu-hood, and so on, leading up to the attainment of Brahman, we clearly are entitled to infer that the meditations which the text enjoins, viz. on the different parts of the sun viewed as objects of enjoyment for the Vasus, and so on, really are meant as meditations on Brahman as abiding in those different forms. Meditation on the Vasus and similar beings is thus seen to be possible for the Vasus themselves. And as Brahman really constitutes the only object of meditation, we also see the appropriateness of the text discussed above, 'On him the gods meditate as the light of lights.' The Vrittikâra expresses the same opinion, 'For there is possibility with regard to the Madhu-vidyâ, and so on, Brahman only being the object of meditation everywhere.'
By the way, Adi Shankaracharya also quotes from a Vrititkara whom he calls Upavarsha. He disagrees with Upavarsha in a number of places, for instance on the issue discussed in my question here, which is why a lot of scholars think Adi Shankaracharya's commentary is less faithful to the original meaning of the Brahma Sutras compared to Ramanujacharya. In any case, it's not clear whether Upavarsha is the same person as Baudhayana or whether two different Vrittis on the Brahma Sutras existed.
