It might depend on what happens regarding the Mutilated's reaction to Kellhus' death,
whether and how they change their strategy and how long it takes them to do so.
What do the Mutilated do if Kellhus dies before the final battle?
They think that Kellhus is the insertant. Its possible they just lock the front door and wait for them to either die of starvation or just go home lol. Without contesting the steps and the CWOL, the entire army has to walk over a tiny bridge and fight the dragon, and do it while an army of sranc cut off a retreat.
They actually might make a plan to capture the remaining Anasurimbors - from Kayutas and Serwa to Esmenet and even Mimara. After all, if they thought it had something to do with that family line, they'd probably want to be really careful not to accidentally kill one.
If Kayûtas, Serwa or both of them tried to take control of the Ordeal
The Ordeal is on a pretty tight timeline here. The Scylvendi are coming over the Mountains to the south and east, the New Sranc from the West. They really only have about 12 hours to get people together and Marching.
Either they do that successfully by stomping out mutiny, or they fail and TGO dies where it stands.
So assuming they can succeed, what happens?
TGO might splinter, some might say 'fuck it' and try to go home (I suspect they'd be allowed to), some would certainly die in a power struggle (opposing factions, all that), but at some point what remaining would be stitched together into a cohesive force to March against Golgotterath.
Might be a matter of how quickly they'd manage to get the Ordeal under control in the fallout from Kellhus' death versus the impact of said death on the Mutilated's plans (as I mentioned above).
Hey maybe the rescue Proyas and string up Sorweel in his place? They would be in great need of an Exalt General, so maybe they'd prop him up as the leader and somehow blame everything prior on Sorweel. TGO seems to do well with scapegoats.