Community colleges have near boundless power from the state to do what they want through their school boards, so in terms of those, probably not, because if you make the mistake of giving the government too much power, they tend to keep it and abuse it. I would be startled to find even one Michigan community college with a leave it in your car provision. I've never ever heard of one that didn't have a sweeping weapons ban aside from a select few things, like cops and those in police academies. This is an extremely important thing to try to change.
Universities I'm not so sure about. Aside from the several that I've been told are mentioned in the Michigan consitution, I do not know where they derrive their powers from, nor has anyone ever been able to tell me, so it's impossible for me to say what the limits are there.