I have the halogens. Yes, the noise persists even when the engine is switched off. In fact, the faint noise is there whenever I sit in the cabin. I have no idea whether is actually goes away when I leave the cabin...It's like a ghost.
The noise becomes louder when the front headlight is turned on. The noise will be at its peak when I play iPhone music through AUX (not the iPod connection thingy)