As Tim says, the pitch is judged on its merits. The ball is immediately dead. In yankeesfan's sitch, if the umpire judges the pitch a strike, the (half) inning is over and no run scores. If he judges it a ball, the R3 scores, the BR is awarded 1B, and the other runner's advance.
In other sitches (where the pitch is not strike 3 for the 3rd out of the half inning), any runner(s) are awarded an advance base (whether forced or not)and the ball or strike is added to the batter's count, as judged by the umpire. The batter cannot become a runner on a 3rd strike not caught in this situation.
JM
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