I don't know, and while theoretically an interesting question, it seems like a moot point since I don't know that anyone would do the gruelling work of a presidential campaign, win and then refuse to become president because they prefer some lower office.
This thread deals with this same question about "What happens if someone is elected, but doesn't want to give up their existing office?":
https://talkelections.org/FORUM/index.php?topic=275752.0In it, the hypothetical scenario I posed was one in which the winning candidate *didn't* engage in the grueling work of a presidential campaign, but got some faithless electors, and then the full House elected him because they preferred him to their party's nominee. (In this case, House Republicans in Jan. 2017 preferring Paul Ryan to Donald Trump.)
