I think that the words Boromir said at the Council, "Gondor has no King. Gondor needs no King." could have actually originated from Denethor. After all, the latter probably was jealous of, and hated, Aragorn/Thorongil for quite a long time, and passed on his suspicions to his son. Denethor was also bitter about the fact that Faramir, the "black sheep" of teh family, had inherited the Numenorean blood, rather than Boromir who Denethor loved. I don't think that jealousy affected Boromir, but that resentment probably affected him.
As for Denethor's eventual fate had Aragorn defeated Sauron, knowing Tolkien, Aragorn would have healed Denethor, and let him go wherever he wanted. Tolkien was the kind of man who wanted to believe that everyone had some good left in him, and Denethor did. Perhaps Aragorn's healing would have had a sort of "Bilbo Effect." Denethor would have gone off wherever he wanted and peacefully died.
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But Melkor also was there, and he came to the house of Fëanor, and there he slew Finwë King of the Noldor before his doors, and spilled the first blood in the Blessed Realm; for Finwë alone had not fled from the horror of the Dark.
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