Yes, and the purchaser will dutifully answer the question truthfully.
The way it works here Florida is that the buyer completes the 4473. The FFL then reviews the form to determine if the the buyer is not prohibited from purchasing a firearm. Then the FFL makes a call-in background check with the Florida Department of Law Enforcement(FDLE). If the buyer is denied then the FFL can not transfer the firearm. After 30 days (the appeal time) the local law enforcement agency who has jurisdiction where the purchase was attempted is notified by the FDLE and they pick up the form 4473 and investigate the buyer for lying on the form which is a federal and state felony.
And just think, they started out as mere tax collectors.
You, too can have career success and attain high power if you join in the effort to scare everyone silly and turn the nation into a bunch of pencil-pushers.