I believe that if Denethor survived, Aragorn would still have been made king. People liked Thorongil more than Denethor, and there would be a lot of people who remember who Thorongil was, if Aragorn made that claim. Also, I don't think people would feel much loyalty to a man who insisted that all was lost, when the battle turned out to be victorious. Once Aragorn showed the ring of Barahir, and Elrond brought the sceptre of Annuminas, as well as the whole "hands of a king = hands of a healer" business, people would realise that Aragorn is indeed the rightful king, whether Denethor wills it or no.
Also, Gandalf and Frodo would return as heroes, and they'd support Aragorn for king.
