It is both unprofessional and unethical.
Evangelism is the act of bringing good news to an individual.
Sharing what the Gospel has done in our personal lives is an act of witnessing. Conversion, whereby an individual is given salvation by trusting Christ, is wholly an act of God. No individ-ual can convert another to the Christian Faith. God only asks that His people be faithful witnesses. Several arguments can be made against sharing one's faith in Christ in the context of a professional practice setting.