School insurance kind of only works for when you're on "school duty" :-) If you're not registered, don't have a legit student card updated for that semester, etc. you don't have anything from the school, no library, no recreation/gym, no nothing.

I'm an alumni of two schools and even though I am eligible for all that stuff, I still have to "register" for a period (as alumni, a year usually) to get it.