It appears that the term "emperor" is used in the Safehold series in its modern connotation of merely being a monarch with a higher degree of nobility than a king, which I think is a potentially missed opportunity given how much of the Church of God Awaiting is based upon the Medieval Christian Church.
One of things that used to differentiate an emperor, be he the Holy Roman Emperor of the German People or the Byzantine Emperor, from a mere king was that he did have a role in church administration. (Indeed, while Henry VIII never did claim the title of Emperor, to justify his break with Rome he claimed that historically the Kings of England had held imperial authority like that of Constantine the Great.)
Now, by the time of Grand Fornicator, the Church had obviously eradicated any religious role that either the Emperor of Harchong or the Emperor of Desnair may have once held. Also, using the idea of an Emperor having a religious aspect would have run counter to the apparent authorial intent of the Empire of Charis being a realm that helps establish separation of Church and State on Safehold. Hence, I can see why in the context of the story Himself wanted to tell, He chose to not mention Emperors having a religious function, even one that the Church of God had emasculated by the time Nimue awoke in her cave.
