no, not neccessarily. to visit someone in hospital doesn't always mean they are there for medical treatment, it basically just means that they are situated "in" the hospital. same with to visit someone at the hospital, it's just a different way of saying it!
If he works at the hospital and you went to see him there (on business, perhaps), you would not likely say that you "visited" him there. Anytime I hear the word "visit" with respect to a hospital, I think of seeing a patient. Accordingly, if I heard either sentence, it would make me think of visiting a patient although I'd more often use "in hospital".
I agree with soakupthesun regarding your question about visiting a patient or a worker in a hospital. One additional point: in American English, "I visited him in hospital." would never be said. You'd need to add the definite article: "I visited him in the hospital."