Yes, it will worsen your adrenal fatigue, as any metabolic conditioning program will. Beating the crap out of yourself in a workout just becomes another stressor with which your already overloaded adrenals will have to cope.
When my adrenals get maxed out, I cut back on the caffeine, try to get more sleep, and take ADHS by Biotics Research, available at Amazon. It is really awesome.
Once you start feeling better and your adrenal performance and insulin sensitivity improve, you can ramp up your workouts, if that's something you still want to do.
Otherwise, the fitness principles Mark espouses here should be plenty until you get your other issues in order.