is that the only damage done to the body from radiation.
If it is, then i guess you’re right.
how well does it work?
No. But radioactive iodine is really dangerous, with a half life of 8 days, and it goes right to your thyroid.
how well does it work?
It fills up your iodine storage and the radioactive iodine gets excreted. But too much iodine can make you sick and cause thyroid damage of its own, so don't take it unless they tell you there has been a release from a reactor accident, nuke explosion or, much less likely, dirty bomb with iodine.
No, that’s not the only damage done to the body by radiation.
However, if you want to protect your body from ALL the damage, you are going to have to seal yourself in a lead box or thick concrete bunker. No pill is going to accomplish that.