I just thought I'd clarify that, estimates vary somewhat, but 80-90% of our T3 comes from conversion. Very little T3 comes from the thyroid.
Some people seem to need a little added T3, some seem to need more than a little, and some don't need T3 at all. What works best for each of us depends on our individual makeup.
FYI: If you have no thyroid, taking both T4 and T3 is better than just T4 like Synthroid.
Most of the converting from T4 hormone to the cell consumable T3 hormone is done in the thyroid gland itself. Some conversion is done in other parts of the body. No thyroid- hard to convert - hard to feel optimal.
The short answer: no. LOL
At least not as far as thyroid is concerned. The thyroid builds thyroid hormones from a protein and iodine. No thyroid, no need for iodine.