Given that mongols was pretty much everywhere in terms of religion except prehaps Judism, and the Nestorian heresy (also at that point in time called Asian christianity) was one of the larger minorities, its certainly not unlikely that a Mongol Nestorian Khan makes a powergrab in the westernmost regions, and as an effort not to get piled by both europeans and the Golden Horde, makes the relatively small jump from Nestorianism to either Catholicism or, prehaps more likely Greek Ortodox (given that it Nestorians was closer belief wise to Othodoxism than Catholicism).
Reason for being focused on Othodox, would be that Constantinoble is a closer one to talk to, and they predominantly have traveled though Othodox christianity ... And i believe it would be better if they only took the southen Poland (the north would be defended by a Teutonc Order/HRE Allience), but instead grabbing say, Greater Poland, Mazovia, Hungary, Trencsén, Moldavia and Bulgaria (and prehaps Vidin and Raska while we're at it) to make a spacefilling blob between HRE to the west/North (if they use the attack to incorperate Pomerelia), Golden Horde to the East and the Latin Empire to the south
A protential butterfly from how i'd see it (depending on said Khans powerzone) could be an allience between him and the Empire of Nicaea (or maybe it'll be the reemerged Eastern Roman Empire at that point after the reconquest of Constantinoble in 1261), helping them surive the onslaught a handful of years later from the emerging Osman Sultanate, and/or take over as the successor state of Byzans after the OTL Civil war in 1341, instead of the Serbian Empire