Usually only if the gun is used in a crime or some criminal enterprise, such as a "Straw-purchasing ring".
One offs by baby mamas are usually not prosecuted. There simply isn't enough docket space; you'd need to ignore most other federal crimes and dedicate a significant portion of a given USAO to work straw purchases. I don't work in a USAO, but I'd bet you could double or triple the size overnight of every USAO and federal court in America and there'd be no lack of work.
In general, the lack of capacity in the criminal justice system is a real problem.