Yes it's feasible with no significant drawbacks.
There would be slightly more work to do in establishing a channel, but after keys have been exchanged it's the same old symmetric encryption (ChaCha20 or AES).
The outlook for implementing Lattice into TLS will involve using both pre (RSA/ECC) and post (Lattice and others) Quantum asymetric cryptography in series. Lets call this DUAL for simplicity hereafter.
You then get the mathematical rigour of preQ RSA/ECC AND the highly probable security against Shor's algorithm from postQ Lattice. Having both does increase the time to start a secure channel, but that shouldn't be a problem, the rest of the session uses symmetric (AES and others).
Opportunity to embrace unpatented less-mature lattice algorithms
With this in mind, the maturity of the postQ algorithm becomes much less risky and therefore one could embrace an open postQ algorithm (R-LWE) avoiding patent issues.
Without DUAL, you are open to post-quantum decryption. With DUAL you are only "potentially" open to post-quantum decryption. (Because if they break the postQ part you don't have postQ protection anymore, but at least you still have mature preQ protection for classical threats).
Here are some links to much more detail, that I have written before and shouldn't be necessary for this answer: