Whether the law has any interest in the illegal gun is not the problem. It is still illegal to possess so why would you want it, and like going 40 in a 35 MPH zone, you probably won't get stopped, but if the police want to they can.
(k) It shall be unlawful for any person knowingly to transport, ship, or receive, in interstate or foreign commerce, any fire- arm which has had the importer's or manufacturer's serial number removed, obliterated, or altered, or to possess or receive any firearm which has had the importer's or manufacturer's serial number removed, obliterated, or altered and has, at any time, been shipped or transported in interstate or foreign commerce.