Can I record iPad screen contents over AirPlay to an Apple TV and then recording the HDMI output?

Solution 1:

No - Apple TV (currently) engages HDCP only when needed to protect content that requires HDCP. This is called out in the specifications page as a footnote in teeny tiny grey text:

• Requires HDCP when playing protected content.

You should be able to use whatever HDMI recorder you please as long as the software doesn't detect protected content being played. You can be sure the engineers have considered that they need to pass the HDCP status from say Hulu or rented movies on iOS to the Apple TV when playing protected content. So if you want to record a demo of your normal app usage, this will work well, but not so much for bypassing HDCP by indirection.

If you can gat a computer, a much more robust recording solution is offered in XAleXOwnZX's answer.

Solution 2:

There is a more elegant solution: Reflector

Unfortunately, it is a $15 app, but it serves a perfect function for your case. You can use your computer as an AirPlay receiver, and screen record the screen via ordinary computer screen capture software. No need for an Apple TV nor any cords, just a $15 app and a WiFi lan.