Automate answering the popup for Adobe to "Help improve the Adobe Reader Experience", when launched the first time.

Not via group policy, no.

You need to basically uninstall and reinstall a customised version where you've turned these things off:

For reader X - http://www.adobe.com/support/downloads/detail.jsp?ftpID=4950
For reader 9 - http://www.adobe.com/support/downloads/detail.jsp?ftpID=3993

also an option is to start the AR while in install mode and answer the question once.
then leaving the install mode (per server).
This should  result in a user-registry key saying "question already answered"
If you know the registry key you can rollout this key with AD also.

should be a key like this one:
bUsageMeasurement
"Turns off and locks user participation in the feedback program and disables the UI that controls the feature."
see reference:
http://www.adobe.com/devnet-docs/acrobatetk/tools/PrefRef/Windows/UsageMeasurement.html

Although another way - now you know the relevant keys thanks to dkotte - you could use group policy preferences.

I personally still prefer to use the customisation wizard