Don't have a rule book handy at the moment. Maybe I'm confused. I thought it was up to the defensive team to decide if they wanted to take the result of the at bat or the incorrect batter to be out.
FED and ASA now the same on batting out of order. If the defense property appeals a batting out of order, the batter who should have batted is out, not the batter who actually batted. If any outs are made due to the incorrect batter putting the ball into play, all outs stand other than an out made on the incorrect batter. The incorrect batters at bat is essentially negated and the batter who should have batted is declared out. Any advance of runners or outs made while the incorrect batter is at bat prior to the ball being put into play stand.
If you are on defense, you do not want to appeal the batting out of order until the batter has completed the at bat. If you appeal it before, the correct batter simply takes the place of the incorrect batter in the batters box and assumes the current count. If you wait to appeal it until the at bat is completed then the batter who should have batted is declared out and the incorrect batter removed from base. Any runners forced to advance, or who advanced because of the ball being put into play by the incorrect batter are returned to the base they occupied.