What is "an NFA?" NFA refers to the National Firearms Act of 1934. So, the answer is no. You also don't need a Gun Control Act of 1968.
Purchase the barrel, give it to your 'smith, and have him mount the comp/brake to bring the length to 16". Then mount the barrel in an upper and stick it on a rifle.
ETA: with regard to constructive possession, there's a difference between possession of a barrel, which cannot be simply slapped onto an AR, and a complete short-barreled AR upper. Buy the barrel and take it to your 'smith.