Now, a better question is if the new President had ever really been the VP for more than a nanosecond.
That would have to be the case for that individual to have succeeded to the Presidency, unless otherwise placed at the top of the line of succession. The VP-elect takes the oath of office before the President-elect, just before noon. At noon, the Presidency would be officially vacant and the new VP would presumably take the oath of office as President of the United States. It would be redundant, but I think it would be necessary to take the oath of office almost back-to-back for Vice President and then President.
They'd become President at exactly noon, and would never be VP.
