I haven’t heard that usage before either.
Googling, it looks to me like it (possibly only?) exists in a set phrase… “I don’t care if school keeps or not”, “I don’t give a damn if school keeps or not”, “whether school keeps or not” etc. which is used in situations where no actual school is involved to mean something like “come hell or high water”. Where’s that coming from I wonder?
It seems to me that “Whether school keeps or not” is based on the idea that in severe circumstances, schools are closed, eh? So “whether school keeps or not” is a fairly straightforward rendition of “under any circumstances.”
If that’s what you were asking....