It's been done before in my fraternity. Apparently, the President-elect one year was inelgible to be President because he wasn't enrolled.
So, the VP at the time got promoted (my gosh, he was fsckin' incompetent) and we elected a new VP.
It wasn't a great time because our fraternity was near collapse at that point, and our secretary went AWOL -- I had to take over the secretarial duties in addition to my already overwhelming duty as treasurer.
-MK