NICS is electronic and don’t think for a second that ALL state and federal agencies haven’t created databases to contain and search that data. Every firearm purchase goes through NICS. They already have this information and use it.
As an FFL I am well aware of what goes to NICS and what doesn’t. Right now the only information transmitted about the firearm is whether it is a handgun, long gun, or other (e.g. stripped receiver). Under the e-4473 more detailed information, such as the make, model, serial number, and caliber, would be available to the ATF.