does the second general have effect on troops on battlefield?

[Omanes Alexandrapolites]

I'm not too sure about that redriver. In my experience, if the main general dies/runs away, the second guy simply acts as heavy cavalry - he never seems to take command. However, he still, strangely, gets traits out of the battle such as Good Commander, even though he was not commanding it. The same is often true for Captains and the man-of-the-hour event - my Captain died, but the new Captain of the army gained the prestigious reward of adoption.