I crouched as Dark Pit with the missiles and noticed I could still fire them. I can also fire them upward. Not sure if this is Classic powerup system only though.
The real question is could Pit use the Hammer while crouching in Kid Icarus. Probably not, but it's worth looking into it.
My current save is in a castle, I'll get back to you. EDIT: He can't. He also can't use it when looking up.