As has been stated many times before on this forum, when a long gun is transferred in California, serial number info is not on the CA DROS that goes to the state. Serial number info for long guns is recorded on federal form 4473 and retained in the FFL's records. So the short answer is no, it's not like they can access a database and type in a serial number to find the owner. The long answer is yes, all it takes is a phone call to a FFL to get information on guns that he has transferred.
The exception to that is when a FFL goes out of business and turns over his records to BATF. If that particular FFL ever transferred a gun to you, the feds have your info. I heard a rumor that CA DOJ has tried to get access to out of business FFL records to track down unregistered assault weapons, but I don't know if that's true or not. I wouldn't doubt it. It wouldn't be the first time state and federal DOJs have shared information.