I agree that it is unlikely that university employees/faculty probably wont be in the first round of vaccinations as essential employees.
I agree that the government purchased the vaccine and that there will not be a charge for the vaccine. (However, depending on how or where the shots are given, there may be an administration fee for those giving the shots, but insurance should cover that, and otherwise, it is not likely to be more than $25, tops).
I dont think that the vaccine will be required, though. However, I dont think that the university will be as eager to keep providing accommodations for those requesting online classes once the vaccine is available. IF you choose NOT to get the shot, you can not require the university to provide you special scheduling.
As for students being required to get the shots, I dont think that the university will do ANYTHING to keep students (' tuition dollars) from returning as quickly as possible.
The combination of the faculty being able/required to teach in person, and students not being required to take the shot, I think that there will be sufficient motivation for faculty to get the shots. Students are still at the 'invincible age' and as they have generally not had significant deaths, or in the case of asymptomatic spreaders, any negative affects, they may be slow to take it, and even if they wanted, would likely be lower on the list gaining access.
Just my thoughts. Im sure that the devil is in the details.