Wow, yeah, that's a really good question on your part, Kristen.
I am leaning toward what Kate has said, and would agree. At the same time, I am not sure about its use with breeding birds. In my thinking, when given pellets it is often suggested that no other supplements are required, really. This much I know for Harrison's Organic Pellets.
I have introduced small bird iodine blocks before because my birds don't eat enough of their pellets and are still mainly on seed diet. So, they don't get enough there either.
As far as breeding goes, eventually both parents will feed the chicks and so what they ingest, they will pass on and I am not sure how this might impact them. As Kate mentioned, overuse of supplements with pellets can create more problems with the potential for too much vitamin/mineral intake, but I would definitely be interested to know what your vet might think on iodine block or supplement use.
My birds only get the block once in awhile and actually prefer it over their cuttlebone, but mostly they nibble what they want, when they want, and it works for them as a beak conditioner (destroy it).
So, keep us informed. I certainly would like to know more.