I had a Catholic acquaintance who attended a school like this once. He said it turned out disastrous for two main reasons. One is that, despite it not being in the rules and regulations of the school, when they found out he was attending another Church service besides their mandatory ones (mass, of course), they began to fine him for it anyway. Other people attended outside services that were baptist or generic, too, but were not fined. Just him, the Catholic. Secondly, despite being an excellent student, it became apparent to him very quickly that part of his grade was based on his personal beliefs, meaning that as long as he remained Catholic, no matter how well he did on assignments and tests, his grades were so poor that he could not have graduated with a degree. He got passing grades, but you have to have at least a 2.5 in your major, and they weren’t giving him that.
The point is that I highly recommend against it. It is their job to “save” you from your Catholicism and attending school there gives them HUGE power and authority over you and it is extremely easy for them to manipulate you like they tried to my acquaintance.