I think those beard scratchers better get back in those books of theirs, I don't think you can serve as Vice-President if you could not be elected to the office of President.
Article XII ratified in 1804 states..... "But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States."
Then Article XXII comes along and is ratified in 1951 limiting the terms a President can be elected to with the presidency with the following..... "No person shall be elected to the office of the President more than twice, and no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be elected to the office of the President more than once"
The question I guess could be argued that he isn't being elected to the Presidency when elected as VP and would succeed to the office rather than being elected again.....