Yes, the same way how people in the US trade at European exchanges, even though it's night in the US. And in practice, one of those reasons is that the exchanges aren't open 24/7: If I can't get a trade through at an European exchange because they are already closed, I'll just buy the stuff at an US-based exchange instead, if this one is still open.

But to be honest, the whole question is irrelevant. Let's consider all major exchanges are based in the US (which they aren't!) and all of them close during the night. How long do you think would it take for a new exchange to open in Europe or Japan that does not abide to those closing times? And in reality even existing exchanges won't abide to this: MtGox is based in Japan, Bitmarket is based in Europe, etc. So why should they abide to US timezones?