To the best of my knowledge, the catholic church considers civil marriages as invalid.The tribunal would have to verify the invalidity of that marriage. This process would be an easy and a brief one.
The church can still prohibit you from being remarried for various reasons or have you go through a process of discernment and counseling prior to getting remarried again.
I think people often think, well I've got my annulment, so now I can get married again. No true. The church can and often does place conditions with your annulment for sacramental marriage in the church. Until those conditions are met you may still not be able to get married in the church. It's case dependent and called a VETITUM placed by the court of first instance and confirmed by the second court. You need two positives by the way.
Not to scare anyone............