To be honest, if it's the What-If continuity, no, I don't think you should. Just like previous players rarely have a say of who get the character after they do, unless it's an underground trade. Depending on how long a character stays with a player, usually the character has had continuity made up between numerous different players, so it's no more their character than it is the game's.
Now, for the case of characters that have stayed with the player since the beginning of the game, I guess it mostly depends on how said player feels. I, personally, would have no issue with anyone else coming in to play Ultimate Batman for a What-If season, if I were not willing to do so myself. But someone like wiegeabo might have a problem with someone else strolling away from what he did with Sinestro in a What-If season of DC. But, the truth is... why should that player care in the first place? It's an alternate continuity. Nothing done in the What-If season would affect the actual canon of the regular one.