Well I am anaemic and I have to take the iron pill while on my period because I tend to get weak and tied. If you don't have anemia then then really isn't any reason to be taking the iron pill. And I'm pretty sure that the iron pill doesn't harm you.
Use of iron like Ferrous gluconate or Ferrous sulphate without any reason can harm you. During periods, iron deficiency can occur due to blood loss. But it is not necessary to to take iron unless you bleed heavily and for longer duration. If you are having normal periods and not anemic then taking good diet will compensate iron loss during periods. Otherwise you can take iron. So, always use iron after discussing with your doctor.