Sure, but it'll prevent a civil war and I'll point out that the Ulricans haven't AFAIK, actually properly schismed in the past, so while it might not have entirely solved their issues, they seem to have generally settled into a status quo.
I rather doubt it'll come to an actual armed conflict. For one, there's no actual contact line where such a thing would happen, as mentioned in the update. It would take deliberate effort of arming up and marching. And that would get the rest of the empire involved, which neither party wants. Given the signs of chaos rising, you could easily be accused of doing so to aid chaos in weakening the empire, at which point either the Witchhunters, the Lights or the Greys might come around. No, it's pretty clear this is a political conflict. Says so in the update too:
With the physical borders drawn right down the border between Nordland and Middenland - a narrow and heavily forested strip of land hemmed in by the Middle Mountains on one side and Laurelorn on the other - the matter will not, thankfully, be settled by violence. The only way this comes to a conclusive end is if one side is able to garner enough support of the wider Cult of Ulric to drown out the voices of the other, and thus the attention of the two factions is turning to the farflung branches of the Cult.
As for not having schisimed in the past? Well, I disagree. Kind of depends on what you see as a schism, of course, but for my money the Nordland and Middenland Ulricans had
already schismed long ago, and this is just that coming to the fore again. And the Ar-Ulric going to Talabecland and then having to return to Middenland probably looked a lot like a Schism to the people at the time. The first is definitely big enough to be called a schism, and I don't think enough is known about the second to be sure.
But it's not like there was just one Ulrican faith at some point, and then there were two. It's schisms all the way down. You have the really big ones, like Nordland/Middenland. But within those you have various subgroups with different takes. Then you have subgroups in those (like the "make stores in preperation" vs "burn down stores in preperation" extremists). And if you cared to look, then there's no doubt subdivision in those groups, which are only relevant to the members of the group. And so on, and so on. And in the end, you'd find there's more Ulrican faiths than there are Ulricans, even if a whole lot of them are quite similar. But when it's about religion, ie the fate of the soul and the world as far as the adherents are concerned, those differences that seem like irrelevant details to outsiders can drive people to murder and martyrdom. I'm not going to give IRL examples because politics, but then I don't think I need to either.