I agree with the assumptions behind your question. A supposedly more efficient heater is merely one that reaches working temperature faster, so you gain when you switch on and lose out on the storage heater effect by the same amount when you switch off. There is no point in worrying which appliance is converting electrical energy to thermal, as they all do in the end. The intelligent approach is not to purchase more expensive appliances, that probably wasted more energy in their production, if you always have heating on. Of course, if you use air conditioning in summer, that is a completely different matter.

You are absolutely right. Any device releases heat as a by-product, and will act to reduce the need for an electric heater by the same amount. All electric heaters are equally efficient in the production of heat/kwh despite the claims of various manufacturers. Adding a fan may make you feel more comfortable since it can move the air around and help prevent the hottest air from accumulating near the ceiling, where you do not benefit from it.