Supposedly this issue is right now before the Supreme Court.
But, this is not a hypothetical. It has already happened. Barack Obama ordered the assassination of Osama bin Laden. It was carried out by US special forces.
As detailed in the movie, Zero Dark Thirty, the special forces entered the bin Laden compound with a body bag – fully intending to bring their target back inside it. When they confronted bin Laden, he was not armed; he made no attempt to resist; and he was in the presence of women who were also unarmed and who also made no attempt to resist.
After the invasion team shot bin Laden and he was on the floor, they shot him one or two more times just to make sure he was dead. The team returned the body bag to their base camp, and later he was dumped into the sea.
As far as I know, the movie is consistent with all known facts and I have never seen any refutation of it.
The reason Hollywood didn’t like the movie was that it showed the US locating bin Laden partly as a result of information gained through torture. This same sentiment was reflected in a New York Times editorial on the event.
After praising the assassination (but not calling it that), the Times went on to say:
Much will be made of the fact that the original tip came from detainees at the prison at Guantánamo Bay, Cuba. There is no evidence that good intelligence like this was the result of secret detentions or abuse and torture. Everything suggests the opposite.
In other words, assassination is okay, even admirable. Torture is not.