What are the consequences of belligerency?
1. If an individual is a combatant under the laws of the war, he/she is a military objective. Military objectives do not enjoy protection as civilians. They can be targeted by military operations. The President's order is directed toward that end.
2. If the individual is rendered hors de combat i.e., is captured, surrenders, or is injured, he can be tried under a military commission.
Attacking a combatant is not an "execution" in the proper sense of the term. Authorization to target a combatant does not require a trial. The Laws of War apply in this case. The Supreme Court has spoken on that matter in the past and it is extremely unlikely that the Supreme Court will reverse its longstanding precedent.
In sum, the President's authorization is constitutional.
But not in matters of warfare.The Constitution supersedes any treaty in matters of American law.
The Constitution does not apply in war zones.Ergo, the Constitution applies and the Geneva Conventions do not when it comes to the treatment of American citizens by American authorities.
In other words, no treaty can ever supersede the Constitution without an Amendment stating such.
I'll concede this point.The supremacy is implicit at first, because otherwise federal laws which are judged unConstitutional could not be struck down by the courts.
The supremacy becomes explicit later in the Article, since it says judges are not bound by treaties in any instance where said treaties contradict the Constitution or federal law.
The Fifth Amendment makes a specific exception for "cases arising in the land or naval forces".5th Amendment. The government cannot deny a citizen of the United States of life, liberty or property without due process.
Additionally, the prohibition against stripping life, liberty or property without due process proceeds that initial statement, which makes it clear that due process is still required.