It isn't too far of a stretch. Right now, biometric companies are working hard to do a Minority Report-style system so marketers can target you when you enter a store. The store displays suddenly switch to show you things you like when you enter, that sort of thing. They really don't think of the Feds at first when they do these things. Heck, I've already put a few beacons around some of the venues we own which send custom messages to returning customers' phones when they enter the premises.
One of my fears about the NFA system is that we're all beta-testing a future registration scheme for guns in general. Well, if that's the case, we're proving such a scheme would never work. The Feds have issues with the few million NFA items out there, how would they handle a few hundred million?
But yeah, imagine this - your likeness is digitized, and companies can hook into it. Suddenly you're banned from IKEA because you may or may not have a gun on you, but IKEA has access to the Fed's facial database and when you entered, it ran a query and got a hit. No Klerjöppøer for you!
Haven't you noticed that when you swipe your credit card or debit card at the gas station the indicator light blinks on the type of fuel you usually buy..before you actually flipped the lever. System already knows from previous fill ups.