Then he probably is. It would make sense - Captain America was the best the Allies have on the table, including France, England, Russia, and everyone else. As Captain America, he'd have to give out orders on the field without getting snarled in military protocol.

Which would be hella awkward after he gets defrosted. After Omar Bradley died, the rank was discontinued - Steve can technically command every single allied army that is currently fighting on our side. I doubt that would make them happy.