Kage is traditionally the strongest but not necessarily so yes, based on his ideal of protecting the village.
Though honestly, while people will say Tsunade managed to become Hokage without being the strongest, she was. According to the databook info, she had the highest stats, and in a straight-up fight there was really no one in the village who could have definitely beat her at the time. Kakashi might have had a shot and now we know that Danzo had some tricks but no one else really. This is not counting Jiraya as he was doing his solo thing at the time.