If you want to be technical, then the scenario is simply impossible, even if the "starter" gets 0 outs because the pitcher who starts the game is the starters. If Buch was on a 40 pitch limit or something in that range, he'd simply be a long reliever being used for a few early innings in the game.
Another scenario from a few years ago.... Dice-k was scratched minutes before his start, and Atchison (who wasn't stretched out as a long man at the time) ended up starting the game, and the bullpen pitched the entire game. Not a playoff game obviously, but the Red Sox have done it before.