Does the run count?

Yes

The umpire screwed up by making a double call. Once the BR was put in jeopardy by his mistake he should have killed it and placed the BR at first. So yes the run should count.

ahhh Mechanics...........the longer I umpire the more I am sure that most if not the vast majority of umpire errors are because an umpire has used poor mechanics.........

In this case, a well timed call would have eliminated the double call that led this umpire into this problem....

See the play..... make the call.........verbalize the call.......it only takes a second longer, but in most cases it makes the difference in being right the first and only time.

Like MST has posted, this is fixable and should have been.........