What would happen if I took a course without instructors “permission”?

I want to take POLI 311/313 but to take the class, POLI 210 (or equivalent) is required, or you can get the permission of the instructor to enroll. The thing is, I did actually take POLI 210 last year but I failed the course (for a very complex and stupid reason which I don't feel like getting into lol).

I know that I can just ask for the professors permission but I feel like they will immediately say no (which they have every right to). However, let's say I do take POLI 311/313 and I get a good grade (or at least pass), would it show up on my transcript? Would it impact me when I apply for graduation? I know that I can just retake POLI 210 but I'd have to wait until next semester and I really want to take a methods course ASAP.