IPad – Turn off iPad 2 screen mirroring

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.

From Apple's Apple TV 2 AirPlay page (in the footnotes at the bottom of that page):

1. AirPlay is available on all devices running iOS 4.3 or later. Some features require the latest software. Second-generation Apple TV or later required.
2. AirPlay Mirroring is available with iPad 2 or later; iPhone 4S; iMac (Mid 2011 or newer), Mac mini (Mid 2011 or newer), MacBook Air (Mid 2011 or newer), and MacBook Pro (Early 2011 or newer) with Mountain Lion.

This explains your situation as far as what you're describing, which sounds like mirroring. In my experience with the 1st gen iPad, there is usually a speaker icon next to the name of your Apple TV when you are attempting AirPlay and audio-only capability is available. When you're using hardware with video AirPlay capability (i.e., Mirroring), there is a TV icon next to the name of the Apple TV. Beyond the footnotes listed above, this is a sure indicator of your iPad to Apple TV connectivity options.