Timed Plays and Appeals

[ahudgins21]

Play that happened last night:

Adult Softball - USSSA

1 out, runners on 2nd and 3rd. Batter hits deep fly ball to left field. Left fielder makes incredible catch at the fence. Runner on 3rd tags up, scores easily. Runner on 2nd thought the ball was dropped, so he has already touched 3rd, rounded it, then realized the ball was caught. He goes back to second, without retouching 3rd. He is thrown out going back to 2nd - 3rd out. As of now, the run counts because its a timing play, not a force out, correct? The question is, what if the defense appeals the runner missing 3rd on the return to 2nd? Does the run still count?