Plus, ATV out of the box cannot stream Pandora.
Au contraire!
If you have an iPad, iPhone, or iPod Touch you can use Airplay to stream the audio to the ATV. With Pandora active, double-tap the "Home" button, and scroll to the left to reveal the AirPlay icon (the one with the "up" arrow) and select the appropriate AppleTV.
The audio comes through great, however there is no artist or song title, nor is album art displayed on the TV screen. (Presumably you can get this info from the handheld device you are holding.)
As far as the original question ("Can you run an AppleTV without a display?") I'd double check first. I just tried turning the TV off, while leaving the A/V receiver and AppleTV on - and got nothing. It may be that the AppleTV needs a signal from the HDMI connection that it is attached to a powered-on TV.
I'd experiment further, but having recently spent many, many hours getting all my connections
just so, I'm hesitant to start playing around with cables.