Licensed FFLs have no way of running serial numbers. Serial numbers are logged on an A&D book when stores acquire the weapon, and are reported to the ATF when sold for compliance.
BUT, FFL holders work very closely with law enforcement to verify the guns they are buying from walk-ins aren’t stolen or ghost guns. It’s as simple as calling either a local police department or your nearest ATF field office and giving them the serial, they will cross reference 4473s and the NICS.
So with that being said, there should be some sort of channel of communication between gun vendors and police to verify serial numbers.