Actually, no.
Since Hesburg started the ball rolling when he stole Notre Dame, almost all universities that Catholics built and named as Catholic universities have been put in the hands of a very, very, secular board of trustees and loaded with secular administrators who answer only to those trustees, not to the Catholic Church or any Catholic religious authority.
In fact, Georgetown isn't even supposed to call itself Catholic anymore but given the way US Bishops pretend to be Catholic but mostly aren't, they'll never stop claiming to be Catholic.
Now, I have to ask, were your honestly unaware of the fact that almost all Catholic educational institutions had been considered property illegitimately alienated from the Church (i.e. polite way of saying stolen) since the sixties or early seventies?
It was a rhetorical question.