An interesting one!

I had a similar problem with the cabriolet in the early days after its Turbo conversion, with headlights etc on, when the cooling fan started cutting in and out at idle it would slowly try to stall the engine when it surged on initial turn on, until it did infact stall the engine.

Obviouosly when you turn things on you create a load on the alternator, mine turned out to be a significant air leak which meant when the engine had load on it at idle, it couldnt cope and would cut out.

Presumably your car is MFI?