Force outs

[Guest Peter]

Bases loaded 2 outs. Batter pops up to the catcher in front of home plate. He drops the ball. Runner from home crosses the plate but the catcher throws to third in time to force the runner out at third. Does the run count?

[Senor Azul]

Peter, here is the actual rule that answers your question--

2018 OBR rule 5.08 How a Team Scores

(a) One run shall be scored each time a runner legally advances to and touches first, second, third and home base before three men are put out to end the inning.

EXCEPTION: A run is not scored if the runner advances to home base during a play in which the third out is made (1) by the batter-runner before he touches first base; (2) by any runner being forced out; or (3) by a preceding runner who is declared out because he failed to touch one of the bases.

[umpstu]

24 minutes ago, Guest Peter said:

Bases loaded 2 outs. Batter pops up to the catcher in front of home plate. He drops the ball. Runner from home crosses the plate but the catcher throws to third in time to force the runner out at third. Does the run count?

No.