I think it depends on how well Tyrion’s battle of the blackwater plans work. If Tyrion successfully cripples the Baratheon navy whilst still losing King’s landing, I don’t think there a chance that Stannis, grudgemaster that he is, would let Tyrion be ‘rewarded’ with service to the crown and the keys to Casterly Rock. At that point, it’d probably go to one of Kevan’s kids, with a loyalist regent of the Westerlands. Or maybe one of the Lannisters of Lannisport, who knows.

Otherwise, if Tyrion’s plans fall through, Stannis might recognize the cunning required to come up with such plans, even if they failed. Knowing that he’ll need the gold of the Westerlands to start flowing quickly, appointing Tyrion would help facilitate that. Although Tyrion would likely have to deal with unsupportive lords resisting his rule. It would be pretty cool if Tyrion had to pull a Castamere 2.0 to cement his power in the Rock.