I'm not sure about that. I know that kelp helps both thyroid and adrenals because of all the other nutrients there as well as iodine (natural celtic sea salt is also good for adrenals). As for potassium iodide alone, well that will help low iodine and thyroid, but I don't know enough about adrenals to state what it can do for them. However, improving one glandular function with an element we all need, may improve the rest of the functions (like a dominoe effect).

I know that iodine helps many functions because of what it does for the thyroid and that includes infections and chemical/metal toxicities.

I've posted somewhere else recently and copied and pasted an entire article on nutrients for adrenals etc. I would recommend supporting glandular functions with all elements/nutrients mentioned, as any illness/toxicity appears to deplete these so badly. Many of the ill effects are the result of this.

You could also do a search on the net about iodine and thyroid/adrenals and see what articles you come up with.