At the risk of putting words into mouths, I think their answer would be no. The difference between Hurt Locker and the Catholic church/Cross of Iron/Iwo Jima is that these things are over (really, only the most militant atheists are gonna look at the Catholic church and think, "Fuck you for the inquisition, you totally unchanged institution"), so to consider the problems of the individual soldier or believer is merely to universalize the terrible experience of war. Making individual Nazis sympathetic or even heroic isn't a threat because the institution is dead, and only an expressly pro-Nazi slant would make the film (nostalgically) imperialist.And the real question then to Cocus and Sonmi and others remains: Is this enough? To indict war in general by focusing on the personal/psychological/existential toll on individual foot soldiers? And if it's not, then you'd kind of have to be against other films that have taken similar approaches with politically incorrect sides of older wars, like Cross of Iron and Letters From Iwo Jima.
With the Hurt Locker, America is still around and could possibly start more wars, and thus the threat of the institution is still present. I think Somini's argument was that it's not enough to just say "war is bad" without interrogating the culprits that started the war when they still exist. He seems to think that the film has no criticism of any American policy, and thus implicitly agrees that yes, these soldiers are fucked up but still fighting for "America" so it's worth it. My counterargument is that the film does question whether the soldiers are actually fighting for "America/Democracy around the world". At the film's end its clear that given a choice between war and America, Renner's character will always choose war, and that mindset is why we got into that mess.
If you want my opinion, a far guiltier example of American imperialism (at the time) would be Written on the Wind, or Daddy Long Legs, where the characters are perfectly free to just get up and say they're going to start an oil business in Iran, or join a mining company in South America. I still love the movies though.