If so, could a person auditing a class simply for the sake of learning legally take classes without having to pay tuition?
No, the university is not obligated to let them do so.
The question is very broad because "taking a class" involves many things, almost none of which have anything to do with intellectual property, but I'll try to summarize.
"Fair use" is a concept from copyright law. The basic concept of copyright law is that you may not copy a protected work unless you have the permission of the copyright holder (often granted in the form of a license). But very little of the intellectual process of taking a course involves copying. In particular, copyright law doesn't place any restrictions on your ability to read materials that you receive, listen to lectures, think about them, or write or speak about what you have learned, because none of those things are copying.
Fair use makes it legal to copy, even without permission, in some limited situations where it otherwise wouldn't be. There is some info about the concept here. It is complex and requires a case-by-case analysis based on four factors. Educational use is a positive for one of the factors, but by no means can one say that every educational use of copyrighted material is automatically legal as fair use. If you photocopy a whole textbook, I don't care how educational it is, you're still going to lose in court. Again, though, this is barely relevant, because there just isn't much copying to be done in taking a course.
On the other hand, just because it is not illegal for you to do various things (read notes, listen to lectures, write papers, etc) does not mean that anyone else is legally obligated to facilitate you in doing so. For instance, maybe you are interested in the lecture notes for a course. If you manage to get ahold of them, you may legally read, study, and perhaps even copy them to the extent that fair use permits. But that does not mean that the university or the professor or anyone else has to actually provide you with those notes. They are perfectly free to say "We won't give you those notes, or let you into the room where the class is held, or give you access to the course's Zoom sessions, unless you pay us whatever amount of tuition we demand."