If the thyroid gland just completely stopped working and it went untreated, how long would it take for one's thyroid hormones to get to dangerously low levels? At what point does Myxedema Coma occur?
Hypothyroidism - low levels of thryroid hormones are produced. There are many diseases where hypothyroidism arises. E.g. Graves Disease, Hashimotos disease.
Early observations of Hypothyroidism showed two girls that were born without thyroid glands.
"growth was severely stunted... very little power of locomotion; but could manage to walk from chair to chair with a little assistance. She had no power of speech... no goiter [was present]. The other girl was 6 months of age... was plump but had a marked idiotic expression, a large face with a small head, and very receding forehead. The tongue was large and protruding from the mouth"
One of the girls was 10 years old, which is proof could be a decade or longer.
If you are interested in further reading I would recommend: Congenital hypothyroidism.
New evidence suggests Myxedema coma does not result from hypothyroidism.
Fortunately for 21st century medicine - if hypothyroidism is well-controlled, it will not shorten the suffers lifespan.