I don't think it will harm bone density but I would be cautious of this kind of product for long term use. Supplements like this can cause a cascading dependency. The longer you use them the more you need them. If thyroid hormone is needed it is best to give your body what it needs to produce it. Most people have significant deficiencies that prevent their thyroid from working correctly.
If your adrenals are stressed rest more, meditate and spend time in nature.
Do a search on this forum on Iodine and start reading.
If your thyroid and adrenals are up to speed the rest should fall into line, baring that you actually have all these hormonal glands intact.
"The nurse should be cheerful, orderly, punctual, patient, full of faith, - receptive to Truth and Love" Mary Baker Eddy