I was also thinking from a RP point. I'm just saying that where the Holy Roman Emperor will swear loyalty to the Pope, the Evangelical Patriarch swears loyalty to the HCC Emperor. If there were a need for the Emperor to be crowned by the Patriarch, refusing to do so would probably be seen as treason, meaning the Patriarch would lose more legitimacy than the Emperor.
Huuum I see, that kinda makes sense when I think about it, since the Protestant Church has been born partly because of a rejection of the Pope and the Papal power in general.
I will still push my idea with a slightly different approach : I could see the Patriarch trying to elevate himself on Papal-like levels if the Crown authority is weak or inexistant and if the Emperor is a bad one, that could be an interesting event where the main Patriarch (which is called President in the mod I believe) takes power. But that's an idea for another day anyway