Coverity helps almost not at all for concurrency problems.
It can help identify cases where you don't lock when you should (by showing that all the other users of a thing acquire a lock). It can show you when you seem to be holding a lock when others release it. It can't do much for any more complex concurrency errors at all. It really doesn't even try.
You can *write* checkers for coverity that try to do things that are more sophisticated, but typically they have to be somewhat heuristic for your own local set of problems. And the going is rough, because the documentation is rather thin on the ground. Really, having the source would probably be more helpful than the documentation which currently exists.