I can't speak for in people, but in cats there are a lot of serious consequences to being hyperthyroid and not treating it. Chief among them being anatomical changes to the heart muscle that can lead to heart failure, increased risk of thromboembolism, gastrointestinal upset and hypertension (which can lead to retinal detachment if untreated).

I had a friend with Grave's disease (hyperthyroidism) and although she lost a lot of weight, she had terrible mood swings and felt awful all of the time. Her heart was always racing and her blood pressure was through the roof. The thyroid affects nearly every cell in the body and I imagine that being ramped up all the time can't be good for you. But then again, I only treat animals so I don't know for people. It would definitely be worth a discussion with your physician, I think.