No, she couldn't.
According to the twelfth amendment of the Constitution, "no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States."
Having already served the maximum allowable two terms as President pursuant to the 22nd Amendment, Clinton is constitutionally ineligible to be President again.
Bill would argue that he was elected twice, he definitely cant be elected President again. But if he were VP and POTUS was incapacitated, he wouldn't be elected, he'd be elevated. It doesn't say someone can't serve more than two terms, it says they can't be elected.
As for the 12th amendment: "But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States."
Clinton would argue "I am ineligible to run for the office but not to hold the office. Thus the 12th amendment does not apply."
Who wants to bet the SCOTUS would wave him right on through?