It would be an interesting experiment to use Iodine homeopathically. But if you have a potentially serious disease such as fibrocystic breasts or thyroid problems, I's stick to Iodoral or Lugol's.
That being said, the only way we could really test a homeopathic is if the person taking it got bromide detox. The effectiveness of Iodine is usually judged by its ability to displace bromide, even tho not everybody gets detox.