So it seemed in the seventh century.It was a different world by the 13th century.
A Mongol-founded world religion could certainly convert most of Central Asia, where Islam was not yet fully consolidated. Iran might be a possibility depending on the stability of the alt-Ilkhanate or the religious affiliation of an alt-Timur, and with Iran and Central Asia converted, it is quite likely that large areas of India would be converted in due time. Since the Manchus would probably convert, an alt-Qing dynasty could make a large proportion of China follow the faith even if the original Chinese converts were purged by the Ming. This alone would make as much as 15% of the world population follow this hypothetical Mongol religion.