If Genghis Khan had managed to unite all the mongol tribes, and there is some paltry evidence suggesting that he nearly accomplished this, it would be possible, with a lot of luck, conquer China, although in the long run the Mongols would be assimilated.
OOC: I think we're assuming he united a few tribes. If he hasn't united all the tribes, would he still be called Genghis Khan? IIRC, doesn't that mean 'Universal Kahn' or 'Wide-Ruling Khan' or something like that?
Please, it would take lottery odds for the Mongols to conquer mighty China!