I had this same problem when I tried it - No output from the AirPlay even though the display was shwing up and the output device was "Apple TV" in fact if I went to the sound preference panel and attempted to increase the volume, the AirPlay did play the beeps that preference panel emitted. I called Apple support and they were unsure ar first that this capability is even supported. They had me try to reproduce the problem with a new user account. In my case MainStage did work with the Apple TV under the new account. So, they recommended that I quit MainStage, then delete the MainStage-related plist file in my home directory's library/preferences/ folder:
After deleting this file, I relaunched MainStage and was able to get the Mainstage output on the ausio system attached to the airport. The delay encoundered is excessive - unsuitable for live performance for me, possibly dud to the fact that I am using an 802.11g wireless connection rather the faster 802.11.n connection. It works fine otherwise.