I've run without that part for ages mate, no drop in power... I removed it because it wouldn't sit properly and didn't want it destroying itself in the rad fans. I'm not usually a big fan of CAI's, although I've had two on the GTI, but anything to get rid of the standard bloody airbox arrangement, which is a pain to remove a pain to fit, and if not on absolutely perfectly can pull thetop of the oil filler cap off; as well as straining other areas of the induction, like you've shown.
