The thyroid treatment is expensive, but $3000 sounds very high--it was about $1000 for Spot, and that includes the x-rays, urine test and echocardiogram.
How quickly they decline depends on the cat and the progression of the disease. The thyroid hormone levels send their metabolism into overtime. Their heart, kidneys, and other organs have to work harder and faster. It gets to a point where they can't take enough enough food because they are using so many calories--that's why they lose weight. Spot was treated with radioiodine, but it didn't work for him. He was off of the medication for two months before I insisted on starting him back on it again (Spot was a special case--most cats respond to the radioiodine treatment but Spot got worse instead). Before treatment, he was almost 11 pounds. After two months without medication, he weighed a mere 7 pounds 1 ounce, having lost more than 30% of his body weight.
I would strongly advise against not treating the cat. If the thyroid levels are high, it is the equivalent of allowing your cat to starve to death. It would be more humane to put a cat to sleep than allow it to suffer--I did that as well with a stray who had FIV and hyperthyroidism (a neighbor later claimed he was her cat...but that's another story). There at least one case that I know of where someone had at least some luck using natural remedies (called glandulars) but I don't know how well it would work long term.
As for the cost of the medication, you can find better deals by getting the prescription from your vet and shopping around. Check with local pharmacies. Drugstore.com offers 100 tablets of the 5 mg methimazole for $37.99. That would last for about 3 months.