Presumably not - if anything, they'd be natural allies, with some quite clear spheres of influence and shared interests in the south of the Rus' lands. A Turkish Rûm is potentially possible (though religion would complicate any claim of the Imperial title), but it has sort of been done to death on this site - the one where they ended up ruling all the way to the gates of Vienna was particularly egregious.
Alright, but I maintain that OTL was a bit of a Serbia wank. The Despotate of Thessaly was never going to survive long after the Crusade set it up--it was just luck the Serbs snapped it up first, and from there their whole "Empire of Serbs and Greeks" concept began gaining steam. If you had asked a Greek or Serb peasant of 1300, or even 1350, if they thought the Serbian Empire would encompass Constantinople and western Anatolia they would have laughed in your face. The Muslim Turks could very well have held on to the Anatolian plateau if it weren't for the conversion of the Karamanids and their horse archers.
And oh, geez,
The Gunpowder Caliphate is the most blatant wank I have read on this site. Magic "Ottomans" wipe out the Mamluks! Magic "Ottomans" hold the Haemics for centuries! Ugh.
Wow, that would really muck up Polish history. Without the Ascanians conquering Poland and introducing many Teutonic settlers to help jump start Poland's urban economy, you are going to have a very different country. I mean, the ruling house had heavily Polonized within three generations, especially after the ascension of Dytryk I when the capitol was moved back to Krakow, but they never lost their westward leaning outlook. With no Ascanian conquest, would Poland be as involved with the western markets and economy?
You're right, Poland would be unrecognizable. I suspect it might end up like Ruthenia (southern Novgorod) did, with serfdom entrenched, powerful nobles, and an Eastern focus. It certainly wouldn't have been the powerful military and dynastic player of OTL--no Game of Thrones,* most likely! Austria would've "gotten away" with more dynastic shenanigans too, probably--no Franco-Polish alliance in the War of the Hungarian Succession, for instance.
*OOC: The Game of Thrones was a protracted struggle for dominance in the various petty states of the HRE between the Habsburgs and Ascanians through marriage