I'd be surprised if they do more than mention that epsilon-delta stuff exists. Most AP calc classes have very little epsilon-delta work. We spent maybe two or three days on it in mine, certainly not enough time to write a full proof, and that was more than most people I've talked to who did it at different high schools. If my experience is at all representative, that rigorous of a development of calculus isn't normal until upper-level classes, when you're heading towards analysis.