He says he will come. Someone, whether it be a male or female, is telling someone else that "he" will come. Where the person is coming to is understood by both people involved in the conversation. "He" has also been established beforehand, and recently. It could be that two people are talking about a movie that they want to see, and they have invited several people to go with them.# John: Do you know if Frank will come to the movie with us? Sandy: He says he will come. Here, John wants to know if Frank has said whether or not he will be attending the movie with him and Sandy. Sandy's reply is that he (Frank) has told her that he plans on going to the movie with Sandy and John.

Yes He says (that) he will come. [it’s reported speech. It means that he has said, probably more than once, that he (himself or some other male; it’s not clear what “he” is being referred to) is going to come sometime in the future.]

Yes, it's correct. It's correct because it's a normal thing to say.