For the "Anytime" tournaments, you just need to join and pay your fees before the start time. Then you have 24 hours from the start time of the tournament to submit all your battles, so "yes" you can get some sleep.

For the live tournaments (the ones that do not display "Anytime"), you need to check-in start at 15 mins before the tournament start time, then you need to battle live. These are actually the old style of tournaments and are pretty fun, but there are not too many of these around anymore.