Not really. People don't get tossed out of school for plagiarism because they're violating someone's copyright. In fact, you don't need the notion of intellectual property at all to have the independent notion of academic integrity - one is significantly older than the other.
My high school calculus teacher put a copyright on his exams. He didn’t need to—copyrights are implicit. But it communicated the point.
Your high school calculus teacher wouldn't have flunked you if you copied your neighbour's exam answers because you were violating their copyright. They'd have flunked you because you cheated. If someone in Ancient Egypt sent their cousin to sit the Obelisk Chiseling Guild exam for them and got caught, same thing. None of this has anything to do with 'intellectual property'.