"Nazi leadership had a war to inspire the public so they didn't really need Hitler, and could make much smarter decisions in his absence, and so the Nazis actually win the war "

Since fanatism and not smartness were the desired traits in the Nazis, I doubt they would have made more smart decisions - rather infighting with the national conservative part of the Wehrmacht and society taking over. (thanking the nazis for the plain power base they build them and getting rid of democracy and then kicking them out, like they planned from the beginning and reinstall a king)