Can polycythemia in a child cause mental illness in the future?

Depends: Polycythemia(pc) is a term used for multiple conditions. A transient benign problem in infants; inherited increases in red cell production(treated with blood removal) or a cancer like problem. Increased RBC mass can plug the pipes & injure brain or other areas, making instability more likely. The stress of a chronic disease can create mental problems, the more serious the disease the more likely.

Possible but rare: Polycythemia, which mostly is an increase in red blood cells but can affect other blood cell lines as well, has multiple complications, mostly physical. There are rare reports almost always in adults of acute onset of psychiatric disorders such as psychosis or depression. This could be secondary to strokes, which can occur because the blood is "too thick.".