ASA Rules Question From Prospective Ump

[greymule]

Here's a related play. How would you call it?

Abel on 3B, Baker on 1B, 2 outs. Charles lines a hit to right field. Abel scores. As F4 takes the throw from F10, Baker stops on 2B, Charles stops on 1B. As F4 is walking the ball in, Baker, wrongly assuming time is out since play appears to be stopped, goes back toward 1B to retrieve his hat. F4 tags Baker, and since time wasn't called, you call Baker out for the third out.

Does Abel's run count?