But that's just it, the loophole would be that he is eligible to be president, but just that he can't be elected as such. It's pretty dumb but the phrasing of the 22nd does use the word "elected", clearly we all know the intent but the words may have undermined the spirit.
Either way, both the VP and the president have the same stated basic requirements, but the 22nd amendment makes no statement of the VP. While common sense suggests it's dumb to have a person that hit the term limit as VP, it is not expressly codified.
So no matter the interpretation of the 22nd amendment, it seems like he could be VP. If you have a sane interpretation of the 22nd amendment as a hard term limit, then the succession would skip such a VP, just like it would skip a foreign born person.