If I remember correctly from childhood (I was chemistry-geek six year-old when Chernobyl blew up and the radioactive cloud drifted right where we were living at the time, but there were lots of talks about it later on), the idea is to saturate your thyroid gland with non-radioactive iodine, so that it won't absorb the nastier kind. It offers no relief from other types of radiation.
Fission products include Iodine 131 which is radioactive and would concentrate in the thyroid thereby irradiating the thyroid over time.
The idea is to flood the body with an excess of non-radioactive iodine so it won't keep any I131 that it comes across.