I'm going against the grain here, and recommend against it. For most people it's not an issue. But I've got some issue with my wrists (undiagnosed, but my brother and mother both have tendinitis in their wrist, so that's my guess). I also used to play drums and piano. Something I noticed was that days after doing judo or bjj when we went heavy on wrist locks, I was in too much pain to play for any significant amount of time for the next day or two. Nowadays I don't play any instruments, but somedays my wrists will definitely still feel 'achy' the next day, and gaming can sometimes be an issue.
Never anything that caused a main issue, but I also wasn't a professional drummer, and this was while I was a teenager/early 20's, so relatively quick healing still. If I went back to playing piano or drumming, and especially if I did them professionally, I probably wouldn't do BJJ. And that's ignoring the risks of hurting fingers, where a finger sprain could absolutely put you out of commission for a bit.
I would recommend going with a different option, but if you really want to try BJJ, wait for a day you know you aren't going to be in a studio for a day or two, then try it out, see how it feels and how playing drums feels the next day. If you really want to test it out, also ask if you can learn some wrist locks to have them try it on you.