Obligatory Anandtech explanation on Catalyst AI:
http://www.anandtech.com/show/1488/2
The summary or that is basically...
Catalyst AI = Finding ways to take shortcuts that have the most minimal impact on image quality for rather large boosts in performance.
So from my understanding, the applications that benefit the biggest from Catalyst AI are games that are most poorly optimized for running on AMD's graphics hardware.
So in theory, seeing performance boosts by using Catalyst AI is *BAD* as it means you should go back and change your game to make it run better on AMD hardware.
Not seeing any performance boosts from using Catalyst AI on linux games is in fact, a good thing as it means the games already are optimized well for AMD hardware.