Not necessarily. It would have to be litigated, but if Harvard makes a case that this is punishment for their contisutionally protected free speech, then they are likely to win in court. The administration would have to prove that Harvard is harming it’s student’s civil liberties, and not that they are saying things he disagrees with. Given the scope and breadth of the demands, as well as the administration’s statements, Harvard should be able to make a compelling case that the administration is punishing Harvard for not backing a political narrative favored by the administration.
Obligatory caveat that I am not a lawyer.