A friend of mine carried a sawed off shotgun as a Marine in Vietnam. I have seen pictures of soldiers in Iraq with sawed off shotguns. These days they are outfitted with folding stocks, lights and other tactical goodies but they are still sawed off shotguns.
Don't think so...Sawed off refers to barrel length not folding stocks. The sawed off shot guns laws are actually minimum barrel length requirements. Typically sawed off weapons are used by gangbangers as robbery weapons and intimidation weapons.
Then it wasn't a military issue weapon. The standard issue SG in Vietnam was the Remington 870 Express, a 12 gauge pump. The modifications weren't length but chokes, duckbills, stocks and camouflage. There were a few Winchester and Stevens but they were 12 gauge pumps too.