RJD2

2 outs, runner on third, 2 strikes on batter. Next pitch is breaking ball in dirt that batter takes half swing at and ball gets away from catcher. Runner from third scores but catcher appeals that batter went around on swing. Umpire calls strike 3 so batter takes off for first base. Catcher throws batter out at first for 3rd out well after runner from third scores. Does the run count?