The run counts since it is not a FORCE PLAY. It is considered a TIME PLAY. See the top pf page 5 at the following website:
mlb.mlb.com/mlb/downloads/y2008/official_rules/02_definition_of_terms.pdf
"A FORCE PLAY is a play in which a runner legally loses his right to occupy a base by reason of the batter becoming a runner.
Rule 2.00 (Force Play)
Comment: Confusion regarding this play is removed by remembering that frequently the “force” situation is removed during the play.
Example: Man on first, one out, ball hit sharply to first baseman who touches the bag and batter-runner is out. The force is removed at that moment and runner advancing to second must be tagged. If there had been a runner on third or second,
and either of these runners scored before the tag-out at second, the run counts. Had the first baseman thrown to second and the ball then had been returned to first, the play at second was a force out, making two outs, and the return throw to first ahead of the runner would have made three outs. In that case, no
run would score.
Example: Not a force out. One out. Runner on first and third. Batter flies out. Two out. Runner on third tags up and scores. Runner on first tries to retouch before throw from fielder reaches first baseman, but does not get back in time and is out. Three outs. If, in umpire’s judgment, the runner from third touched home before the ball was held at first base, the run counts."