To answer your question, no. The BR must reach first base and all other Rs forced to do so must advance at least one base to have a time play come into effect. In your stitch, the BR never reached first, so no run.
My question back is why was the BR called out? The ball was dropped, so that's not it. You didn't say she entered the dugout. I can't believe she possibly interfered with the right fielder's play. So I have seen nothing to call her out on yet.
-Josh
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