Do not get sucked into a first amendment arguement with the student. Their need for attention has already consumed too much of your energy. The student is free to email his peers or speak face to face with his peers or telephone his peers. Nothing is stopping him. As a previous poster stated, YOU have the responsibility to determine what is appropriate and professional on a course discussion board, comparable to the CHE fora moderator (or the US Supreme Court if his rant included anything about bong hits for Jesus). I second the suggestion to break off the email exchange and require the student to come discuss it in person.
Yes, yes, yes! If a student in a regular classroom kept talking to another student, and you told them to be quiet, would you be denying them exercise of the First Amendment protected free speech? Absolutely not. You have the right to moderate the discussion. In fact, you have a duty to moderate the discussion. And on the very slight chance the student does show up to talk to you, say just that.