On Mountain Lion, an AirPlay icon appears in the menu bar whenever a suitable video output device is connected, and the device will appear as a selection. If it does not appear, then there is a communication problem between the Mac and the display device that can be difficult to diagnose.
I don't question the corporate animosity you describe but I doubt it extends to preventing AirPlay mirroring from working properly. Usually it is a matter of configuring your display device to recognize the external input. Make sure you are using a compatible adapter, if that is a factor in your application.
Use System Preferences > Displays to determine if the Mac detects the presence of an external display.