And no, you don't have a Fifth Amendment to not be shot at when you join the enemy during a war; and no, being a citizen does not give you rights, and the Constitution does not grant you rights. The Constitution grants the government powers and limits those powers. All people inherently have rights by virtue of being born. Read Blackstone's Commentaries; the Founding Fathers did. That was the standard law textbook in the colonies at the time of the Revolution.
Remember that this whole drone nontroversy arises from the killing of al-Qaeda's leader Anwar Awlaki and a few of his followers who all happen to have been US citizens and who had invaded Yemen and carved out their own country there. The drone question is not about hypothetical harm done to innocent Americans, it's about whether the army may use military force on al-Qaeda when there is a Congressional law explicitly directing that the army do so. Why is this even a question?