As noted by the last poster a "registry" already exists (and has for many, many years) in the form of NCIC... Any officer can find out very quickly whether a firearm is reported stolen (and a "stolen" entry lasts years and years, cuts across every state line, etc.). In the event any offender is foolish enough to attempt to alter, deface or remove the serial number that's an arrestable offense the moment he/she if found in possession of that gun....
In my years on the street I recovered quite a few reported stolen weapons (and a few that hadn't been reported). A few of them were originally reported stolen years and years before I came across them.....
The giveaway for anyone considering purchasing a weapon that might be stolen is when the seller does everything possible not to identify himself to the buyer (and I would want solid I.D. to record before ever making a purchase -if the purchase is from an individual instead of a store or shop.....