How effective is iron infusion in raising blood count? how soon can one expect to see improvement?

Several weeks: If you have anemia due to low iron, increasing your iron level will help in the production of new red cells but it takes time for the bone marrow to release these cells. Normally red cells live for 120 days, bone marrow can increase the production if needed as in case of anemia due to iron deficiency, but only after iron is available. From that time it may take 2-4 weeks to start improving.