From what I am reading is that if you have an ARC and don't have a re-entry permit then you have to surrender the ARC every time you leave and apply for a new one when you return. If you do have an ARC and are on a student visa, I don't think there is anything much that can prevent you from applying for a re-entry permit (even though your visa is a multiple entry visa).
If in doubt go out to or call the Immigration Bureau and see.

As for the item of a re-entry permit overriding a invalid visa, I do not think that is the case, if a visa becomes invalid, then the re-entry permit that came along with it also becomes invalid.