If the president elect dies before being sworn in...

[Joe Republic]

No.  At noon on January 20th after the late president-elect's election, the office of President is instantly considered vacant, and therefore the new VP (who would have just assumed that office technically at the same moment) would immediately become President.

Now, a better question is if the new President had ever really been the VP for more than a nanosecond.

[Joe Republic]

I'll also add that taking the oath isn't even necessary.  For example, LBJ became president the moment JFK was pronounced dead, not when this picture was taken about two hours later.  Or for another example, there is a long-standing myth that David Rice Atchison, the next in line to the presidency in 1849, became president for one day when Zachary Taylor refused to swear in until the next day after the designated inauguration day.  Oath or no oath, Taylor became president the moment Polk's term expired, and Atchison was never president.