I just passed the level I exam in June right after graduating and the CFA Institute wouldn’t even allow me to register for the level II exam until a few weeks ago when they confirmed that I have my bachelor’s degree. I don’t see how it would be possible to get registered in time after passing level I when you can’t confirm your degree until around May (depending on when your graduation date is).
But like everyone else says…focus on passing level I before even thinking about level II. You have your whole career, and to be honest, you probably wouldn’t have enough time to study for level II in that small time frame if you pass level I, espically while finishing your senior year.