Since there is no agreement among historians over who was the first Pope in history to take any form of Papal Oath, and there have been several versions which apparently have been used, and it is not now nor prior to Vatican II was it part of the official rites of the Coronation of a Pope. Will you define for us two things.
Which version of the Oath are you referring to?.
Would you deny the Papacy of all Popes before the 7th Century who never took such an oath, as well as Popes after Pope Paul VI, because they too did not?
The Church holds that the Oath and the Coronation do not effect the legitimacy of the Papacy. The moment a bishop who is validly elected accepts the office he is Pope, with all the authority of the Office. If a layman, man in Minor Orders, or Major Orders who is not yet consecrated a bishop, he assumes the full authority of the office once he has been consecrated a bishop. This applied before Vatican II and after both.