Can Apple TV work over network only, without the need for HDMI
No, the Apple TV video output works solely via HDMI. Audio can also go via optical out. The Apple TV is an AirPlay receiver. What you are suggesting is an AirPlay transmitter, like the iPad and iPhone are, which send a video or audio stream to an AirPlay receiver, like the Apple TV. You won't get around to connecting the Apple TV to the actual display with HDMI. 

The Apple TV itself is very small, so you should be able to mount it next to or behind the TV / display. Hiding the Apps is only a cosmetic change. If you don't provide a remote, and set a screen saver which shows e.g. your corporate logo, people will probably not even see the apps, but still be able to connect to the Apple TV via AirPlay.