My '07 GTI does the same D$#! thing. My car is currently all stock. Any time that I idle (with or without A/C on), I here a noise start that gets progressively louder, runs for a while, and then winds down. It is much more frequent when the A/C is running.
I took it to the dealer and had them listen. They said it was a secondary air pump kicking on and that it was normal. However, as others have said, I never noticed this in previous years of my ownership, and now it is much more frequent and louder. i do not trust the info that I am getting from the dealership.
I am thinking of trading for a Mazaspeed 3, because I just can't stand the noise anymore.