If it's an unarmed strike, it synergizes, and there's no reason for them to be the exception given they could of just gone the route of the Aarakocra.
Well, Volo's says it's an unarmed strike that does 1d6+Strength mod piercing or 1d4+Strength mod slashing.
I think a DM could right (but lame) to declare you get either the Martial Arts benefit or the racial, and cannot max-and-match them — like how AC calculations work.
The wording doesn't clarify how these interactions work, so while it's clear how players want it to work, no one can use RAW as a club on this one; you'll need to talk to your DM.