Run score or out?

Well let me take a stab at it, just for fun.
It wasn't a batted ball that hit the runner3, so no out on that rule.
R3 was clearly stealing home when he was hit by the pitched ball.
Can anyone other then the batter runner be in the batters box?
or at the plate when the pitch is thrown?
Was it a pitch are a pick off throw?
Did BR or R3 come in contact with the catcher?

I would have to say both runs score. But could be wrong?

Interesting situation indeed! My inclination is to say that:
- the pitch counts as a ball
- the run counts
- the ball is dead
- runner on 2nd goes back to 3rd base (if he was stealing also -- otherwise back to 2nd)

FYI, here's a ruling from OBR that isn't exactly the scenario you described, but it's pretty interesting.

"With two out, a runner on third base, and two strikes on the batter, the runner attempts to steal home base on a legal pitch and the ball touches the runner in the batter's strike zone. The umpire shall call "Strike Three," the batter is out and the run shall not count; before two are out, the umpire shall call "Strike Three," the ball is dead, and the run counts."

I think the last part indirectly supports what I stated originally.

Let's see what some of our resident experts say.

Actually, RPD did a pretty good job on this with one exception...whether the runner at second was stealing makes no difference in this case.

If a runner (in this case the runner stealing home) is touched by a pitched ball, the ball is dead and runners are awarded one base from the base occupied at the time of the pitch. Assuming that the ump called the pitch a ball or a strike that wasn't strike three; the runner stealing home scores and the runner who was on second goes back to third. If the runner on second had already touched third at the time of the pitch (very doubtful) he would be awarded home also.

Pilsner is exactly correct.