I have a question about a run counting

[GreenSuedeBlue]

There are two outs and there are two baserunners on second and on third
The batter hits a grounder to the Shortstop and doesn't run to first base. The runner on second gets in a pickle between second and third while the runner on third touches home base. The batter starts running to first base and the runner who was on second base is tagged out. The third baseman who made the out throws the ball to the first baseman before the batter gets there. Does that run count??