How do you know you don't have adrenal fatigue?
maybe because there is no such definitive documentable syndrome of this "fatique" that you specify, that exists?
OP - yes iodine supplementation has some unique and specific benefits, and there are some in the medical community who feel we suffer from a mass epidemic of iodine deficiency (due to a great many factors but not least of which is poor fortification of processed foods)
but that said: this is not an area where you should just stumble around and experiment..make sure you are well-versed and educated in correct parameters of such, or seek guidance from someone who is themselves
I do applaud your thinking outside the box here however!