The fate of Corporal Woodson (spoilers)

Did anybody else get the vibe that Woodson healed from his wounds and survived? For some reason - I interpreted the hospital scene as Woodson and Blocker saying goodbye to each other not because of the notion that Woodson would succumb to his wounds and die, but because both Woodson and Blocker knew (at least at this point in the story) that Blocker was going to commit suicide in the near future.

We never fully find out if Woodson died from his wounds - in a movie that does not pull punches in regards to significant characters being killed off left and right, I feel like the ambiguity of Woodson surviving/dying is certainly a hope spot. That along with the fact that it was shown early on in the film (when Blocker goes out to the field area and unholsters his pistol as he screams at the sky, right after he was briefed/assigned his mission) that Blocker clearly had wrestled with suicidal ideations. Seeing as how Woodson and Blocker were close friends, Woodson most likely knew about Blocker's suicidal thoughts/depression.

Did anybody else get the impression that Woodson survived?