Here's a 5.56mm barrel with a 1:5" twist. I never heard of one that fast, but since it's only 5" long, you get exactly ONE revolution before the bullet leaves the muzzle. Even with that fast of a twist, it doesn't seem like one revolution would even begin to stabilize it. I'll bet the bullet has a lot of yaw to it, even if it does fly straight. And, unless your ammo is loaded with fast powders made for use in such an abbreviated barrel, It's probably not going to burn much of it. I think any ammo would be subsonic from a stubby barrel like that, and MAYBE the powder would continue to burn as it flew between the baffles of a suppressor. But, I'm not sure that's how that works. An integrally suppressed barrel would be way better than that slapping a can on this abortion of a barrel. You would have 10.5″ effective rifling for 16.5″ OAL barrel with a MISB AR upper from SWS Rifles, instead of 5" of rifling with a suppressor screwed on in front of it. It would be more accurate, and you would only need one tax stamp instead of two since it's not an SBR.
P.S. If the stroke of the bolt carrier is longer than the distance from the gas port to bolt face, how reliable is your gun going to be? It might work with one weight of bullet in one brand of ammo if the gas port is reamed out large enough, and the gas tube can handle that volume of gas in such a short amount of time, but this just looks like an invitation for malfunctions.
P.P.S. I want to see this set up as a short barreled M16A2.