The run doesn't count.
OBR
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.
Young_Ump's post in 3rd strike steal of home was marked as the answer