The post-Zero Hour Hawk God one probably could, and I think that recent Hawkman series retconned Barbatos as one of Hawkman's incarnations, so... As far as classic superhero versions of the character, though, no. Comics seem to go back and forth on whether he's just a regular guy using weird science and magical gear or has innate superhuman qualities as well, but even in the latter cases he was never one of the heavy hitters.
That said, I think what the movie did with him worked extremely well, and they needed someone who was able to go toe-to-toe with Black Adam in a physical fight, even if at an advantage. Hodge's performance felt more in-character for the Carter Hall I remember than any live action adaptation I've seen previously, even if the particular details of his superheroics deviated from the source material.