He's suspended. Suspensions for accumulating yellow cards only cause bans in the same competition, but red card suspensions affect any domestic games. Likewise, if we get a player sent off tomorrow, he could miss (a) league game(s).
If a player gets two yellow cards in the FA Cup he misses the next FA Cup game, but existing yellow cards get wiped after the quarter-finals, so you can only miss the final through suspension if you get a red card beforehand.