Later in Act 3, Hamlet tells Gertrude he must be "cruel to be kind." Is there any possibility that Hamlet wrongheadedly seeks to push Ophelia so violently away that she does leave Elsinore, in order to protect her from the violence he knows will follow?
I don't think Hamlet ever considered Ophelia would leave Elsinore. It wasn't done for young ladies unless she was wed to a nobleman from another country. He does push her away from him emotionally since he has an inkling that he will not survive the fray. In this way, Hamlet seeks to protect her emotionally as well as physically.