The irony is the only gun owners who stay below the radar are ones who buy from private owners or buy guns illegally. In other cases, the background checks and paperwork licensed dealers must complete ensures the government pretty much knows who owns guns and the kind. Even if gun owners didn't register their guns, the government already knows where they live.
I'm not sure, but I think those dealer records are probably all on paper (non electronic), and wouldn't the government have to subpoena every single gun dealer (that is still in business) in the country to get that information? Doesn't the government purge from their system the link between a NICS check and the particular individual after 7 days? I think that was a stipulation placed upon the NICS checks when the Brady Bill got passed. I'm just going off what I recall reading in the past. Correct me if I'm wrong.