If you have concerns about using your university email address, you can apply without. However, you will have to provide sufficient documentation to prove your enrollment and there can be a substantial delay as the team verify your documents.
You can, of course, use your university email on GitHub but not use it in a way that will be displayed publicly. We have more information here:
Using someone else’s university email address to apply for the pack is considered fraudulent, and if discovered, usually carries substantial consequences in terms of your ability to use GitHub.