Re: Can an argumentative essay have a title with a question?
Welcome to Using English.
If I were your teacher, I would say yes, as long as your argumentative essay completely answered the question with persuasive arguments in favor of your answer.
A more standard title might be: The Death of John Smith: An Elaborate Hoax
If you are concerned, you can always check with your professor and see how it's received.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.