Most people think that caffein is stimulating directly the adrenals but here is cause and effect mixed up.
Caffein acts as a catalyst to promote the burn up of carbohydrates, that is the main function and this is also the reason why caffein hast anti-diabetic-effects. Caffein is just a efficient Sugar into energy converter, there is no harm in this effect.
The adrenals get only involved when there are no carbohydrates which can be burned. Then cortisol is raised because of a dramtic stress situation: The body needs carbohydrates to burn them up but there are no available and Sugar in the blood gets to low. The raise of cortisol brings the body into catabolic situation, the body now tries to feed itself of itself, e.g. protein-structures and some fat will be mobilized to convert it into sugar. The procedure will ulitmatively lead to exhausted adrenals and lower energy auxiliary.
The danger in caffein is not caffein itself but rather the way people drink their coffee. You must drink coffee with eating food (carbohydrates and proteins rich food) otherwise it will not give you its effects.
As I said before caffein has some healthy effects, e.g. anti-diabetic, anti-estrogenic properties (serotonin, trypthophan lowering mechanism) and it also prevents the absorption of iron from food and increases renal excretion of cadmium.
Nothing is harder on the adrenals as unbound heavy-metals. I would also suggest everyone to do at least 3-6 times blood donation to lower iron in the body if your doc allowed it. Iron is itself strong inflammatory, doing the adrenals no good, the same applies for copper.