Can homeopathy bring additional benefits to thalassemic patients on hydrea (hydroxyurea)?

No: Truly homeopathic "medications" are made by repeated dilutions, so that the ingredient is not really in the medication anymore (just the "essence" of it remains). That means there is no active ingredient left to cause any benefit. However, that also implies that the homeopathic "medicine" should be pretty harmless, unless some other non-homeopathic ingredients were added.

Yes, actually: This is an area of active study -- and so far has positive results. http://www.ncbi.nlm.nih.gov/pmc/articles/pmc2816384/ in this publication, 38 thalassemic patients on Hydroxyurea therapy were given individualized homeopathic remedies. There was a significant decrease in the serum ferritin, and an increase in fetal hemoglobin levels in the combined, treated subjects. Splenomegaly decreased too.