What if Golden Horde succesively becomes a Christian Orthodox empire ?

Suppose that Sartak, Khan of the Golden Horde, which adopted Christian Orthodoxy from Rus', because of this is not poisoned. Tatars gradually converts to Orthodoxy and khan took the title of Tsar. How further relations will look with Rus' and Tamerlane? Whether there will be a chance for a peaceful unification of the two Orthodox nations? Is the Golden Horde could replace Russia?
 
The butterflies are sad that so many of them had to die to preserve Timur.

And why would the khan take the title of tsar?
 
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