I imagine the NCAA would have a pretty easy "out" to not allow a combined AK athletics program split across two campuses. "If Hawaii can do it, AK will need to play within the current rules as well..."
If the politicians stuck to their guns and don't provide another solution other than these drastic academic cuts, I don't see any way athletics survives at one or both schools. As was noted above, just cutting the big dollar sports isn't the answer because you need to replace them with other sports to have the minimum number of sports.
I think it is sad that one campus (or both) could potentially lose athletics because for most students, that's a big part of the college experience. However without a collegiate athletics program, is it any different than attending a community college where everything is club teams? Are you going to school for a degree or for the fun times? Hopefully athletics at one school could be saved. If you just want a degree, go to no frills UA1... if you want the full blown university experience with way higher tuition and some sports teams that need to be supported without the government's help, then you enroll at UA2.