The Hedjet definitely doesn't stop the ghost from spawning on the XBLA version. (In particular, you'll have to dodge the ghost if you want to spend a while blowing up the City of Gold!) I can't recall if I've gotten a dark level while wearing the Hedjet or not.
On the plus side, it's easier to get the Hedjet; as far as I can tell, dying anywhere in any way on the Moai level will spawn you inside it. Even blowing yourself up or falling off the bottom of the level work.
Last edited by SnapDragon; 07-08-2012 at 08:50 PM.