It is legal to mark the barrel. A guy who goes by "Shade1" over on UziTalk got a letter from tech branch about this. His Uzi SBR has his name/city/state on the bottom of the barrel. I have seen pump shotguns done the same way here in Ohio.
Remember once you have that stamp, the receiver is a NFA item regardless of where you engraved it. If you take the barrel with your name/city/state and temporarily change it with a 18+ inch barrel it probably wont be a big deal. Its a lot more fun if you don't get caught. If you want to sell it as a title 1 firearm you still must have the gun removed from the registry.
Stopping power: The power some guns have to make you stop what you are doing and get your wallet out.