Around the time of the mongol invasion of the middle east, european christians all thought that it was the legendary eastern christian Prester John. This was not the case as mongols were not christians and certainly had to alliance, formal or not, with Christianity.
What if Nestorian efforts pay off and the mongol steppe people are converted? What would this mean for China and the Crusades?
For the Crusades?
I don't know, but it might make it even worse for them as the Catholics are schismatics for the Nestorians from all I know. And the Nestorian Mongols might demand something unacceptable from the Crusaders like changing Catholic rites or something.
Well, Mongols being Christians...
There might be some implications. You see, tengrizm has nothing against drinking alcohol which was the favorite occupation of Chengizz Khan and his offsprings. Actually alcoholism is the main cause of death of the Chengizids from all I know.
The Mongol nobles even chose an official whose chief responsibility was to remind Great Universal Khaan Ogedei not to drink too much (kind of shitty job as Ogedei drank himself to death).
But say that Nestorianism as any Christianity demands some restrictions in drinking alcohol (at least at certain dates) - well, that meaning Chengizz-Khan and Ogedei living a few years years longer - a little longer Western Campaign = a few more European countries screwed, properly screwed, like in Hungary, wasteland and ashes.
But that's what I meant as sort of joke.
On a more serious note -
everything depends on the extent of Mongol Christianization. If it is skin-deep - it doesn't change anything, almost anything.
But I wonder why it is considered impossible for the steppe nomads to be deeply religious Christians. As a matter of fact it is possible if they had baptized a century or so before their world conquest started.
And then the butterflies would have been pretty enormous...