I personally don't think Aragorn would have parted with the company for any but the most dire of reasons. As leader of the company (after Gandalf fell), it was his *responsibility* to see that the given task of the destruction of the Ring was accomplished. To go off on personal quests to become the King of Gondor or whatnot would have simply been irresponsible, whatever his meeting with Faramir might bring about.
However, for the sake of conjecture, if Aragorn had abandoned the quest at Henneth Annun, I don't believe any of the fellowship would have accompanied him (aside for Boromir, of course, had he been living). Sam is obvious. Merry and Pippin would not have left Frodo for the aforementioned reasons. As for Gimli and Legolas--there's really no reason for them to go to Gondor. Gondor was not their home, and they had no destiny to fulfill in Gondor; if they accompanied Aragorn, it would be for friendship's sake. And certainly I think the weight of their assigned task would have taken precedence over acts of friendship.
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