It will still be illegal for him to possess them or even try to obtain them.
The only way to purchase a firearm without a background check (that also isn't an express ticket to federal pound-me-in-the-ass prison) is to buy a used firearm from a private individual in your state. That person also needs to not be a prohibited person themselves, cannot be a firearms dealer by trade, and the firearm must be legal to own in the state in which you both reside.
Online gun sales, new gun sales, and gun sales crossing state lines all require a background check be performed by a licensed dealer, known as an FFL. The ATF randomly audits about 10-15% of FFLs in a given year, which doesn't include the number audited as a part of investigations following up on complaints and tips.
Sorry for the wall of text. Whenever people bring up background checks the uninformed yet highly opinionated tend to come out of the woodwork.
P.S.: If any of said individuals would like to prevent cases that slip through the cracks please write your representatives to increase ATF funding for enforcement activities.
Did you write your representative like I asked or are you just here to vent?