Yes, but music is even harder. I doubt most FPS shooters would suffer much at 60ms latency, but that's an 1/8 note at 120bpm. I would guess that for a jam session to feel OK, you'd want to be <15ms.
Musical tracking has to take special measures to keep the latency low enough even when its all local; see the need for ASIO, jackd, etc.
<pedantic> 120 bpm is 120 quarter note per minute, so a 8th note is 500ms, a 16th note is 250ms, a 32th 125ms. </pedantic>
that said having played with a midi controller on badly configured linux machines i agree 15ms would start to be an issue.
Musical tracking has to take special measures to keep the latency low enough even when its all local; see the need for ASIO, jackd, etc.