Hard to know as these things can vary greatly, but it sounds to me like you'll only get admitted if the program can fund you. Frankly, you shouldn't do a PhD without funding anyway, so that sounds entirely reasonable to me. The fact that an offer may come after April 15 suggests that they are waiting to see if the first batch of candidates who have offers will accept or decline. If enough of them decline, some funding will free up that could go to waitlisted candidates. Whether or not you're officially waitlisted, it sounds like that's what your situation is. Good luck!
