Overall, I too think it would be worth a shot (uh...pardon the pun! LOL) I went and re-read that article and smokey the elder is right about there being a possible downside of developing hypothyroid condition after treatment, but that only affects about 1% of the kitty patients.
However, I do think the advantages far outweigh the disadvantages. Here are a few more points that I found:

How does radioiodine therapy work?

Iodine is an element required for normal health. In the body, it is used primarily by the thyroid gland (located in the neck) to produce the thyroid hormones (T4 and T3 are the two major thyroid hormones).

Radioiodine I-131 is a form of iodine that has been made radioactive. In it's radioactive state, it undergoes a natural process (decay) in which it gives off radiation. The radiation given off consists of three types: alpha, beta and gamma. The half-life of I-131 is eight days; in other words, one-half of the radioiodine goes through this process every eight days.

When taken into the body, a large percentage of radioiodine accumulates in the thyroid gland. The remainder of the I-131 is excreted in the urine and feces. Once the radioiodine is taken up by the thyroid gland (or thyroid tumor in a hyperthyroid cat), the gamma rays and beta particles are released. The beta particles are particularly lethal to the thyroid cells. The beta particles travel a maximum of 2-5 mm in tissue; therefore, beta-particles are locally destructive but spare adjacent hypoplastic thyroid tissue, parathyroid glands, and other cervical structures. The radiation destroys the thyroid tumor cells and thus treats the hyperthyroid condition.

How is the therapy given?

The radioiodine is given as a single dose on the first hospital day. After the treatment is administered, your cat is placed in isolation. In this case, isolation means keeping your cat in a separate "facility", away from other animals not receiving this treatment. Your cat is then monitored over the next seven days until the cat's radioactivity level is low enough to permit his or her return to you.

How long is the hospitalization period?

The half-life of the iodine used is eight days. The iodine is excreted primarily in the cat's urine. The usual period is seven days.

How do I check on my cat's condition during treatment? Is visiting allowed?

Due to the nature of the treatment, visitation is not permitted. The cats are fed and monitored two to three times daily by a full-time veterinary technician during their stay. If you wish, you can call us to check on the status of your cat.

Are there any side effects or risks of therapy?

Since the iodine is specific in its site of action, there is no hair loss or increase in skin pigmentation, as may be seen with other forms of radiation therapy (cobalt radiation). Some cats seem to experience mild discomfort of the thyroid region (thyroiditis) at the beginning of therapy, but this resolves itself spontaneously and does not cause a problem.

Occasionally a cat will develop hypothyroidism (under-active thyroid gland) after treatment with radioiodine. This is easily controlled with supplementation and may not be permanent. Overall, side effects are extremely rare.

What happens after the isolation is over?

Upon discharge your cat will still be minimally radioactive. Even though the level of radioactivity is very low (much lower than the level at which human patients are discharged from the hospital), you should still exercise caution during this period.

All of the remaining radioactivity in your cat will gradually disappear over the next two to four weeks (through radioactive decay and excretion into the urine). Until this is complete, your cat will emit low levels of radiation. Because of this, we require that you also isolate your cat at home for one week further. This isolation can be any spare room in your home.

Much of the residual radioactivity will be eliminated through your cat's urine and feces. Therefore, we recommend that your cat be provided with a litter box that has a liner and is emptied daily. After changing the litter, your hands should be washed thoroughly.

What aftercare will my cat need?

The vast majority of cats require no specific aftercare. Your veterinarian should perform a complete blood analysis after the two week isolation, then monitor the thyroid function three months after, and then on a six month basis as a part of their on-going health care plan for your pet.

Does the radioiodine treatment always work to cure the hyperthyroidism?

Our studies have shown that a single dose of radioiodine is effective in curing hyperthyroidism in over 97% of cats that are treated. Even those cats that are not completely cured after one treatment, however, show some lowering in their circulation thyroid hormone concentrations and improve clinically.

If hyperthyroidism persists for longer than three to six months after treatment, re-treatment with radioiodine is generally recommended to cure the disorder. Virtually all cats that remain hyperthyroid after the first treatment are cured by the second treatment.

Can the hyperthyroidism ever reoccur?

Yes, although it is very uncommon (less than 3% of cats treated). In addition, such reoccurrences usually develop three years or longer after the hyperthyroidism was first treated. Therefore, such relapses may indicate the development of a new thyroid tumor causing hyperthyroidism, rather than relapse from the first tumor that was treated with radioiodine.

What do I do on the day of treatment?

Please bring your cat to the hospital at the scheduled time. You should feed your cat on the day of admission to the hospital (fasting is not necessary). Your veterinarian should have done all or the majority of tests necessary before treatment; if further tests are required, they can be performed by us but treatment may then have to be postponed. If your cat has been on methimazole (Tapazole), this drug must be discontinued for at least two weeks prior to treatment.

Should I bring anything for my cat?

If your cat eats a particular kind of food, we suggest that you bring a few cans so that we know exactly what you want your cat to eat during the time of hospitalization. Personal items (a sock or toy) to place in your cat's cage are not allowed due to contamination.

What happens on the day of admission?

A full explanation of hyperthyroidism and I-131 treatment will be gone over with you. If all of the other routine blood tests have been done by your veterinarian, we will treat your cat on the day of admission.