Nope.
Read the 12th amendment. It doesn't say "elected," it says "eligible."
But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States.
Either by election or by appointment and succession (like Ford), Obama cannot run for nor hold either office due to ineligibility.
-PJ
But Obama is NOT “Constitutionally ineligible to the office of President” (dismissing for the sake of this discussion only his NBC status).
He is 35 years old. He has resided in the US for the past 14 years. And he was accepted as NBC by both major parties and the Chief Justice of the United States in 2009.
The XX Amendment says NOTHING about eligibility to the office. It says he can’t be ELECTED to the office of President. It says it twice. It does not mention the Vice Presidency - at all.
It would have been simple to draft an amendment that said, “Amendment XII is henceforth modified as follows: No person having served more than 731 days in the office of President shall be further eligible to the office, following the completion of his most recent term of service”.
But that’s not what Congress did, and that’s not what the states ratified.