That might not be an enforceable contract. I was trying to look for a case if it ever came up, but I did not see anything, I am just really curious if they are enforceable contracts or not, but I doubt any student has ever sued about it. ... Not to mention the complete unequal bargaining power a applicant has compared to an Ivy League Institution. I just cannot see how these contracts would be enforceable, but I could be wrong.
The answer, of course, is that (as I suspect you were already thinking) these contracts are 100% enforceable - enforceable by reality. As whether they would be enforceable in a court of law, well, that's an interesting academic question - emphasis on "academic."
The underlying reality of most contracts, of course, is that it really doesn't matter what the contract says. In this case, any attempt at pursuing a legal remedy would almost certainly have a net negative result for the plaintiff, regardless of the outcome of the suit.