I'm not so sure they would. I don't think they could afford to take the financial hit if they were to open in the fall and have a considerable percentage of students not enroll for the fall term either due to safety fears or because the students' financial situations have been adversely affected since mid-March. I'm sure everyone will be watching what happens at Liberty U. through the rest of the spring.
I have a relative on faculty at a school about the same size as John Carroll and Mount Union, and that school has delayed budgetary planing for next school year because they are worried about students, especially incoming freshmen, choosing to delay enrolling until the spring semester or simply not enrolling at all for next year. Furthermore, colleges will be doing like everyone else by attempting to cut anything they can from their budgets in order to get their finances back on track without having to touch their precious endowments. There's also the issue of what to do if you're a school with a large percentage of international students (IIRC, my alma mater was 10-15% international). If they went home, when will they be able to return? How do you replace that revenue if they cannot return?
It won't be the case for John Carroll and Mount Union, but some small private colleges were already on thin ice and are not going to be able to survive this situation. I saw an article today about a smaller private college in Illinois that announced it's closing for good. The school was barely hanging on before this situation became the straw that broke the camel's back.
If colleges do open in the fall, I could see there being a sharp increase in enrollment at branch campuses for at least the fall semester.