While it may feel good to review "doom & gloom" scenarios and discuss how you'd outwit the authorities, what I really think would happen would be....
Mostly nothing.
As indicated earlier, it's likely that government agents would move swiftly to categorize gun owners by the
number of guns they own. Those folks would be the ones you'd see on the nightly news getting raided. It would be those large collections they could display in a high school gym floor that would be used to show everyone that we're making the streets safer!"
Other than that, most of us would see nothing happen. They'd be patient enough to wait until you screw up to drop an anvil on you. Screw up as in use one in self defense... then they check your history, find that you owned several and very thoroughly search your home. If they find others, YOU become the bad guy, not a home defender.
Eventually you screw up -- show it to a friend, neighbor, etc. who turns you in or is Mr. Looselips. You give it to your son/daughter when they move out and they get caught with it, so the cops come knocking for you.
More Unintended Consequences:
Drug cartels have, in recent years, attempted to smuggle drugs into this country via
submarines. Plural. They're not especially
good subs, but they do work to stay off the radar. But drug cartels often lose boats, planes, cars, trucks and now subs. If they can afford to lose three $100k airplanes in six weeks they can afford to find clever ways to smuggle guns into the country too.
If they do smuggle in guns, long guns are more likely to be military (select fire) weapons because they are probably easier to get. They'll most likely be cheaper than buying a FA M16 or AK-47 than we have to pay today. Why risk long term imprisonment for a semi-auto gun when you can sell a full-auto for $300 more? Ammo would be from the same source, obviously.
Remember too that guns can be disassembled into many small parts, some of which aren't easily recognizeable.