There are runners on 1st and 3rd, 2 outs, and while a pitch is in progress, the runner on 1st attempts to steal 2nd. The catcher throws to 2nd, and the runner is caught in a pickle, eventually tagged out. During the pickle, the runner at 3rd steals and reaches home before the runner at 1st is declared out.
Does the run scored count? Or does the 3rd out supersede the run scored?