Let me start by saying I suppose this depends on your definition of the word "empire."
Despite that they were militaristic and (necessitated by biology) expansionist, I do not really consider the Yeerks an empire.
They were ruled by the Council of Thirteen, and administered by the Vissers (an appointed position). Which, and correct if I am wrong, was not a hereditary position (I think they were the oldest living yeerks?) This, to me, is an oligarchy (rule by a select powerful few). Or, if they were the oldest yeerks, a genocracy (rule by eldest)
Thoughts?