When the 10th batter hits a ground ball to shortstop, bases are loaded, 2 runs score before player with the ball touches home plate; Do the runs count ?

If I understand you correctly, you are saying that with bases loaded, the batter hits to the shortstop. The runner from third crosses home; the runner for 2nd crosses home; then a defender with the ball touches home. If that is what your situation was, not only do the runs score, but there still has not been an out recorded.

Maybe I am misunderstanding you...

Dixie Rules?
 

In the younger age divisions of Dixie, a maximum of ten batters are allowed to bat. When the tenth batter comes to the plate, there are automatically 2 outs. The inning ends by getting an out or a defensive player with the ball tagging home. Any runs scored before the defensive player tags home will count for the offense.

Re: Dixie Rules?
 

Ohhhhhh..... (scales fall away).... ;)

Yep...this sounds like a Dixie question. Glad to see that ABZ was there to answer it so quickly.

I have also seen this ruling for 8U Coach Pitch in USSSA.