My guess would be "no".
First, how would you prove that they messed up? It's possible that someone either guessed your passed or that it was "sniffed out".
If that's not possible you would still have to prove the registrar created the problem. How would you do that?
My guess is the best thing is to report the problem and see if they have an explanation AND a solution.
You would likely be subject to a registration agreement that limits their liability. It may be a good time to re-read the agreement.
thanks for ypur time