Yes, Lord Byron would be thrown out for acquiring a tame bear. A bear is too large, too dangerous, and too much work to be able to care for in the small confines of a college campus. The risk of injury to not only Lord Byron, but the students and faculty as well, would be to large of a risk for the institute to take on. Not to mention, insurance rates would be astronomical!
While it may have seemed fun at the time to get a tamed bear, we are much more evolved when it comes to animal rights now. Bears have no place in a school or any other setting with people. If provoked a bear could attack, then it would be the one killed.
Regardless of how "tame" the bear is, there is no way that most people would feel comfortable with their next-door neighbor having a pet bear, and there's no way that the college would feel comfortable with a pet bear on college property. I'm not sure if he'd be thrown out, but the bear would have to be taken away.
If Lord Byron had let a dangerous animal lie a bear on a college campus today he absolutely would have been expelled from the university. In today's society we have laws and practices in place to protect the well being of students and teachers. An irresponsible act like this would endager the welfare of others.