Could sickle-hemoglobin c disease be transmitted through blood?

No. This is a genetic disease. A donor unit with sickle-c will not be accepted, and even if you were transfused with such a unit, it would not affect you. If you perhaps had a hemoglobin electrophoresis after a transfusion, and it showed some sickle and some c hemoglobin, you may have been transfused from two donors each bearing the trait.