Do you read my thoughts?

I have wondered - or rather: dreamt - of that for some time ...
Realistically, that requires quite a PoD. The Ottomans followed different policies than in later centuries (e.g. as when they subdued Transylvania as a purely Christian vassal).
I do not think they would have accepted that in Anatolia at so early a point and given their status as a moderately-sized, but quickly expanding realm.
Nevertheless, Hungary' s later fate shows that Christian vassals were possible;
likewise, the longevity of Trebizond in comparison with Constantinople shows that it was a tougher nut to crack.
As for a scenario, I would go for crusaders supporting Trebizond after the shock of the fall of Constantinople. Effective support, however, requires passage over the Black sea; the Ottomans did not endager that, I would think, but questions on feasability remain ...