Yes, a muzzle brake reduces recoil.
You do not need a muzzle brake on a 5.56 AR type rifle. Rifles like the AR15 only have a flash hider.
There are a number of designs for gas operated rifles. The original AR design uses a DI (Direct Impingement) design. There are also a few Piston designs out there.
Keep in mind only a small portion of the gas is used to operate or cycle the rifle. Also, yes, where the gas is bled off in an AR design the pressure is relatively low as compared to for example directly forward of the chamber.
So as mentioned, on an AR the device at the end of the barrel is a "Flash Hider" be it pronged or bird cage type design, it's a flash hider. See Moxie's post #29.
Ron