My daughter is a junior at the University of Dallas, another authentically Catholic college. One of her professors is an alum of Belmont Abbey and he said the same, that they will close it rather than abide by this mandate.
Cardinal O’Connor made the City of New York back down on their insistence on providing birth control and abortions in Catholic foster care homes by simply threatening to close them.
However, in this case, I don’t think it’s going to have any effect on the government. Still, the monks would be right not to accept it and simply close their school. I think there’d be a lot of backlash generated by that.