If we can safely assume that the forum was operated in a professional manner and the psychiatrist intentionally treats members of the forums as he would potential patients, it would be no different from the director of a mental health center treating you after seeing you a few times at local events.

I think it would be ethical for the psychiatrist to treat your friend. However, if your friend already has feelings for him going in, it could make managing those feelings more difficult than it would be if she just met the person. I also think you can't take their relationship for granted. She has seen the psychiatrist interact with other members ("patients") and built a good opinion of him that could be very valuable this early in therapy. I say go for it.