Can increased restless leg syndrome be a symptom of low thyroid hormones due to total thyroidectomy and no replacement meds yet?

Might. When you go through medical literature, you cannot find and paper to find a relation between RLS and hypothyroidism. It actually is a novel idea for research since there is a known relation between anemia and rls, and people with hypothyroidism develop anemia they also might develop rls.
How long ago. Was your thyroid removed? Thyroid medications is very important for your overall health and well being. You may want to try Armor or some other brand that is considered natural. Then you will know if your RLS get better. Thyroid replacement does not change things over night, it may take several months to adjust and find the right dose for you.