Legally he should win. There may be private consequences for speech since the First Amendment applies only to his interactions with governmental bodies. If the University is public it's First Amendment protected, in my view.
He can say whatever he wants. You can say whatever you want. But all actions have consequences whether they are in the open or done on the sly. Look at the number of people in the public that have lost jobs (public and private) over expressing their views or expressing their views in a manner that some deem inappropriate.
ďBe polite, be professional, but have a plan to kill everybody you meet.Ē
James "Mad Dog" Mattis