OP, The short answer; Yes you could buy a completed upper and put it on your lower, but not league! The AR must start life as a "pistol" as others have stated you're converting your rifle to a SBR not a pistol.

Your other question; I have a S&W M&P and it is "mill spec" I don't like that term as it gets tossed around for just about everything AR, it should be "Industry Standard"

As an example I just completed a PCC Pistol Caliber Carbine for Steel Challenge. The manufacture of the upper stated it was "mil spec" I asked them how many 9mm uppers have they sold to the military.