Run score?

[Tru_in_Blu]

Men's slow pitch.

Bases loaded, 2 outs.

Batter hits a ground ball to the right of F6 who fields it cleanly. Since his momentum is going toward 3rd base, he throws the ball to F5 who is moving to get to the base.

R2 assumes he will be out by 15 feet and overruns third base towards his dugout. F5 cannot control the throw from F6 and drops the ball.

Yelling ensues: from the offense telling their runner to get back to the base; from the defense telling F5 to tag the runner.

F5 has retrieved the ball and manages to tag R2 before he can get back to the bag.

R1 has crossed home plate prior to the tag of R2.

Does his run count?