A friend of mine is joining the Catholic Church and is currently going through private lessons with our Priest. My friend has serious health problems and has been told by a doctor that they have done all they can do for him. He is unbaptized and will be baptized next month at our Church. He is really studying the Catholic Faith and has decided that the Priest shouldn’t have anointed him since he has not yet be baptized. Is this correct?
Your friend is correct. Unbaptized persons cannot validly receive any sacrament (other than baptism).
Can. 842 §1. A person who has not received baptism cannot be admitted validly to the other sacraments.