From what I understand, typically audio compression has about 20 ms of ramp-up, though it can be theoretically lowered about ten times — not sure how well it would work in that case, though. Consider that aural reaction speed is apparently way better than visual, wherein the latter is on the order of 200 ms. As is confirmed by musicians hearing a lag of around 15 ms. This leads me to believe that human hearing would probably pick up the shots sound before noise cancellation kicks in, otherwise the cancellation is too sensitive for anything else to be heard.