Every grad school is supposed to give you an answer before April 15th. They all agree among themselves to do so, and there's no provision for a waitlist in their agreement.
I wouldn't count on a school that won't admit you by April 15th admitting you afterwards. If they do, and if you want to withdraw your acceptance from a place whose offer you took, you can do that. The main consequence of doing it is that you can't expect anything from that school again. In other words, if you get in to school #2, accept their offer and then, in May, get in to school #1 and tell school #2 "nevermind, I'm going to school #1," don't expect school #2 to help you out if school #1 sends you an email in June saying "oops, we can't fund you, sorry."
In other words ^2, if you dump a school for somewhere else make sure you have a very firm offer in writing from Somewhere Else.