I can confirm for sure that GP's can demote in war, I just don't know the exact parameters.
In a previous playthrough, I demoted Austria-Hungary as Germany (acquire state CB).
I tried in a second playthrough, but failed to get Austria to demote as NGF (assert hegemony CB).
In my most recent playthrough, I successfully had Austria demote as NGF (humiliate CB).
This is 3.03 HoD, no mods. The wiki states that GP's will not demote in crisis wars. I suspect that they will also not demote in assert hegemony wars. And if you think about, it kind of makes sense, as assert hegemony wars are all about spheres, and you only have spheres as a GP; while crisis wars only happen if you lead or join a side in a crisis, and you are only allowed to do that as a GP.