It would provoke a constitutional challenge the Supreme Court would have to rule on given the text of the 12th and 22nd amendments.Can Barack be VP after being President?
"But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States." - 12th amendment
However, this has never been ruled on by the Supreme Court, and there is an argument that the 22nd amendment permits a term-limited former president to be elected vice-president and then serve out the remainder of the current president's term should they succeed to the office. It's an issue that's been discussed a few times, mostly related to Bill Clinton hypothetically serving as VP after 2000.