ATF does run the "gun trace" when a firearm is recovered at a crime scene. They contact Glockchesterwesson and ask who did you ship this gun to?....Glockchesterwesson then tells them the distributor, who in turn tells ATF the dealer it was shipped to. The dealer will then pull the 4473 and give ATF the info on the buyer. ATF will then contact the buyer in an effort to find out how it arrived at the crime scene. ATF "traces" typically end at the first "private" sale of that firearm because Federal law does not require the seller to keep a record of the transaction.
The FBI maintains several databases, the NCIC is the one that includes stolen firearms. They can try and run the serial number against the database, but it is not uncommon for typographical errors to occur when the stolen firearm is entered or when a gun is recovered:
example:
Stolen gun: "Ruger 10/22 rifle caliber .22 long rifle serial #555-12345"
Firearm being checked: "Sturm, Ruger 1022 rifle caliber .22 serial # 55512345"
Although the information is nearly the same, the missing special characters in the model name and serial number may be enough to mess up the search. ATF mentioned this last year in the FFL Newsletter.