To my knowledge, if you accept an offer from another school and then hear after April 15th on another school, you can most definitely decide to go to that school. You would be out of a deposit though (Which can vary from averages of $500-1000 I believe). I've personally heard of someone that got accepted to a school before April 15th, sent in a deposit, and then got accepted off a waitlist at another school in late April. She declined her offer to school number 1 and sent in a deposit to school number 2. Then in July she got accepted to her in-state and then decided to decline school number 2 in favor of her in-state. That's an unlikely story, and she lost quite a bit of deposit money, but it has the possibility of happening if you applied to multiple schools.
As far as Vet schools seeing whether you have been accepted elsewhere, I honestly don't think that schools do that (If they do someone please correct me), but I do know that you can pull yourself from the waitlist if you get accepted elsewhere and decide to matriculate there.
