I wouldn't use that A1 buffer tube if I were you. The use of any buffer tube that is designed to accept a stock will make it an unregistered SBR, which is why you can't use a normal carbine buffer tube on a pistol unless you machine off the notches and make it incapable of accepting a stock.
Considering a rifle buffer tube can also be used to attach a stock, if you put an un-modified A1 buffer tube on a pistol the BATFE will consider it an unregistered SBR. They make pistol buffer tubes for a reason; they're not designed to accept any kind of stock.
0331: "Accuracy by volume."