From the BATF website: you send in disposition of any criminal records, fingerprints, and $18 and they issue you a UPIN. Whenever you fill out the 4473 you put the UPIN. The dealer gives this number to the NICS employee and they go straight to your record without confusing you with all the other people with your name. I was thinking about doing the same thing. I got a delayed yesterday for a rifle purchase.
I still can't understand why a SSN wouldn't do the same thing. Suposedly, no two people have the same SSN.
Federal Bureau of Investigation - Freedom of Information - Privacy Impact Assessment
.