Can I record iPad screen contents over AirPlay to an Apple TV and then recording the HDMI output? Does the AppleTV HDMI output include any copy protection (e.g. HDCP)? If so, is it always present, or only when playing DRM'd content?

I'd like to use the AppleTV (with AirPlay mirroring from an iPad) as a cheap and simple way to record iPad activity (at a school, for their private use only) by simply plugging the AppleTV into a DVD recorder (no computer is available - so capture cards or other tools needing a computer are out). 

If the AppleTV output is set to prevent recording, what about the output directly from the iPad via the HDMI dock connector ("Apple Digital AV Adapter")? This isn't as convenient, since it's a physical tether to the recorder, but it would be ok (and still cheap and simple).
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.