"Do people with out a thyroid or damaged thyroid benefit from Iodine"
-Yes; the body has numerous receptors for iodine.
Ovaries can to some extent make thyroid hormones. The males have probably a back up system, too.
"Thyroid needs 3% prefers Iodide
(50mg iodide)(hence the high doses for radiation exposure)
Skin needs 20% and prefers iodide
Salivary Glands prefer iodide
Muscles (650mg) and fat needs(700mg iodine) 70%
Breast tissue needs 3-5 mg / day minumum and prefers iodine
Prostate prefers iodine
Stomach prefers iodine
Lungs prefer iodide
Entire body needs 1500 mg 2gm total"