It would depend on the rank and territory. Some territories were considered states, with the head of state therefore having a political function (think of it like the governor of a modern US state). This was the case for many of the assimilated territories like Baden, Württemberg, Saxony etc. Their influence depended on the traditions and constitutions of that particular state and also on the role they were given within the larger German Empire.

Some of them had large military roles because as heads of states they were also considered commander in chief of their respective military like for example the King of Saxony was also the CiC of the Saxon military. However, this was mostly a ceremonial role as overall command lay with the General Staff - units in the field did not have to await confirmation of their orders from the King back home.

However, what you are most likely encountering are the situations in which members of Noble families joined the army or were given field commands. It was common for nobles to join the army, in fact most officers were nobles. As such, their titles normally do not confer any power (this power having been lost over the previous centuries) but are merely titles. The military rank would derive not from the title itself. (commoners who had reached officer rank would also be offered titles unless they came from the free cities of Germany).