If they were serious about finding guns, making examples of people who didn’t register their arsenal then hand them over, tracking them down and making a bust they will and can.
Technically speaking its no different than a drug dealer getting busted for having drugs (and other illegal stuff) at their house. The cops put up surveillance, send in undercovers, DO HOMEWORK ON THE INTERNET, watch the house, the perp, etc. When they have enough of a case they get a warrant and kick the door off the hinges.
All it takes is a few examples and the flood of worried people will register their shit, sell their shit, or as most are still currently, throw their hands up in the air and wonder wtf they are “supposed” to do.