It should work. One of the beauties of this strange little round is that it IS a full pressure cartridge even in subsonic form. The combination of long, heavy bullet and short fat case help keep pressure up. It doesn't have the unnaturally LOW pressure that subsonic .223 and .308 suffer from- since the redced amount of powder has to fill the empty case first before it can move the bullet. Also because of the lack of void, it can use slower burning powders than subsonic loads in normal calibers. The duration of burn is longer and so is the pressure impulse.
It should actually cycle as good or better than a .223 11.5in barrel, and from all I have seen around here the 11.5 in AR's always improve their reliability when they are fitted with a can, since it keeps pressure in the barrel up longer. When you combine a suppressor and .300 Whisper togeather in a 11.5in AR you should get a very very good package, as far as reliability goes. You won't get the full ballistics that the Whisper gets from a longer barrel though. Most .300 barrels out there, for both single shots and ARs, are 14-16 inches in length. Accuracy wise that is a 'sweet spot' for that particular cartridge.