streaming a full screen app or a screen space on apple TV
Unless a hack will be  possible or Apple will have an AirPlay API for someone to make an application that makes the Apple TV a 2nd display it does not look possible with the advertised OS X Mountain Lion feature AirPlay Mirroring, since it will only allow mirroring of what is on your screen, probably only your primary screen too.

Wireless mirroring
Send what’s on your Mac screen to an HDTV wirelessly with Apple TV. Mirroring is great for classrooms, conference rooms, and your living room.