First a rifle, always a rifle. Changing it requires big brother approval, time, cash and registration.
You can get the stamp, cut it down to pistol size, but it won't ever be classified as a pistol. It will be a "weapon made from a rifle" as mentioned above.
From a historical aspect, an Obrez would be pretty cool. As a range toy, it'll certainly be a head turner. Other than that, I don't see any practical use or value to it, but it's your gun and your dime, so if that's what you want to do, then kudos! I'd be lying to say I hadn't thought of doing the same thing.
But what would be really cool, do it with an M44, and reposition the front sight/ bayonet lug on the cut down barrel, and retain the side folding bayonet (maybe cut down to size to match the new barrel length). An Obrez with a 7" bayonet would be historically inaccurate, but badass nonetheless.