Well, you know what they say about that in Cheliax: the Devils are in the Details. :-)
It depends upon just what the Cheliax party is trying to do, and at what point in the (modified) AP. If the Taldor party doesn't have Baba Yaga's blessing, they have to depend upon the Cheliax party at least for entry, although being the way they are, the Cheliax party is probably going to try to saddle the Taldor party with as much heavy lifting and risk as possible. Likewise, the Cheliax party depends upon the Taldor party, although I haven't worked that part out as fully. My idea on this is that initially, they want to keep the Taldor party alive to get information about Taldor government plans (initially they mistake the Taldor party for a Taldan equivalent of themselves); later, they find that they need some of the party's abilities, because (even though they won't admit it), their ideology has caused them to shoot themselves in the foot with regard to certain party abilities that the Taldor party has even if they could wipe the floor with the Taldor party in a straight-up fight (for instance, if they are a party of Hellknights, their tactical doctrine that enforces everyone being in Heavy Armor means that they are going to be BAD at anything affected by Armor Check Penalty, even though Hellknight Armor Training partially alleviates this at higher levels, and so they probably won't have members who are highly skilled at these kinds of things; also, their Diplomatic-related skills are likely to be terrible; if they are Diabolists instead, the first problem is alleviated, but the second problem is probably worse except when dealing with actual Devils or allies thereof).
Now, undoubtedly the Cheliax party has additional goals beyond ending the Reign of winter -- and it is likely that they would be happy to end the Reign of Winter in Cheliax and its vassal states but allow it to continue everywhere else, if they could figure out a way to do so, especially if they could figure out a way to offer relief to any state that would capitulate while keeping the freeze on everyone else until they too capitulated. This goal of theirs must be stopped, even if they are essential to stopping the ritual that is ushering in the Reign of Winter. Something like the World Engine would be of enormous interest to them, and even if they can't repair the particular World Engine that is draining Baba Yaga, they have the potential to gain knowledge needed for building another one. This also must be stopped, again even if they are needed for deactivating this particular World Engine.
Actually would be an interesting endeavor to build and flesh out the Cheliax party as worthy adversaries, but ones that you can't just kill without failing your mission, while at the same time they can't just kill you without failing their mission.