The Fourth Amendment of the U.S. Constitution prohibiting unlawful search and seizure is alive and well and applies to owners of NFA firearms. The ATF or any other government agency must demonstrate probable cause supported by oath or affirmation and obtain a valid search warrant before they can demand access to the premises of an owner of NFA firearms.
The idea that the ATF can conduct a warrantless search when someone owns an NFA firearm probably stems from confusion about the rules that apply to Federal Firearm Licensees (FFL’s). An FFL must submit to a warrantless inspection by the ATF, but that has limits as well.
The ATF can conduct a surprise inspection of gun dealers once a year, but it must be during the FFL’s business hours. Whether the FFL is a dealer of Class 3 firearms or not, the FFL is subject to the these warrantless inspections to check for compliance with the regulations governing FFL’s.