Suppse that the runner at third scored legally, but the runner at second was called on an appeal for missing third. They scored because if you pass a base it is like you touched it(appeal), and you can't unscore yourself themselves. Would the first run count?
Yes. This would be a timing play. Any runs scored before the missed base appeal would count.
If by some circumstance the appeal at third had been force out (say, if bases were loaded to start this play), then no runs would count. But that's not the case here. The runner who started on second was not forced to advance, as apparently the batter-runner was already out on this play.