iron supplement and polycythemia?

Newbie question: Wondering if anyone could enlighten me on the effects of iron supplementation in secondary polycythemia? I understand that the therapeutic phlebotomies lower the blood volume, hemoglobin and hematocrit, thus in turn causing an iron deficiency which is good to a point. My question is: when is the point of supplementing iron a good idea. My husband and I both have secondary PV and have had the phlebotomies and are currently stable. My husband has symptoms of iron deficiency anemia: pagophagia(crunches ice-like 6 trays a day, and carrots, and celery, and raw potatoes), fatigue, restless legs, weakness, etc, etc. He has gone to the doc today for lab work and will return for results in 1 week. But if he supplements iron, wont the H & H go back up and require more phlebotomies? Any info appreciated.