The vast majority of states in the US do not register guns. Georgia does not. As far as a database of fired guns, the only databases that are kept in some LE agencies are samples from guns and cartridges used in crimes. If the gun that was used to kill Mr Dermond was used in another crime, there could be a comparison made with with the fired round.
If a fired bullet extracted was from a body, it would be likely to have an imprint from the lands and grooves in the barrel, along with a measurable diameter. This would identify the caliber in most situations, and narrow down the manufacturer of the gun, and possibly the model. There's no database out there that would link the bullet to a specific gun with a specific serial number, unless the gun was retrieved by LE at some point.