No, the ATF cannot regulate accessories. Pistol braces are perfectly legal to own.
HOWEVER, (and there always is a 'however,') if you own a pistol, and that pistol can accept a brace (because it has a carbine style buffer tube, or other adapter), and you have a pistol brace in a box but not on the pistol, you are in what the ATF calls "constructive possession" and are still in possession of what the ATF is calling a Short Barreled Rifle.
Your pistols must not be capable of readily accepting a pistol brace in order to have the brace be just a lump of plastic and velcro.
So, by the ATF’s reasoning, if you own an AR pistol and an AR rifle of the same caliber, you could be guilty of “constructive possession”? You could, after all, swap a sort barreled pistol upper onto a rifle lower with a stock.