The email you use for school does not have to be your Apple ID, you just need to sign in with your existing Apple ID and change your plan to the student one. Once you've done that it will take you through the process to validate your student eligibility, that may or may not include using your school email. It might just be as simple as logging into a portal like you would normally use to schedule classes.
In any case, for the Apple ID that you use, there is no contingency in relationship to the email you use to validate your student status.