If we get back to the OP, what are the chances of making Joseph Smith, Jr. governor or even president? After all, religious mogul Pat Robertson considered the presidency some decades ago.
The POD will be around 1840. Driven out of Missouri, Illinois welcomed the Mormons. They were sympathetic to this persecuted group. This was their "second chance" to become a function part of a rapidly settling area. Smith could have decided to "tone it down" and be more civil to those outside the faith and thus convince more to join. After all, Smith's assembly of such a large following in such a small time was no small feat. If you are a Mormon, it was a matter of divine influence; in any case, Joseph Smith was an incredibly convincing statesman to his followers. Extrapolating that level persuasion into politics far enough to be a candidate for president is an exceptionally difficult challenge, but not impossible.
Suppose Smith transitions direct control of the church to others, be it Brigham Young, his brother or others. By 1841 he takes a role of integrating Mormon Nauvoo with neighboring counties and communities. My take is that if he was persuasive enough to assemble so many thousands of followers, he could have channeled those talents to present the faith and community as a functioning part of Illinois (and Iowa).
That century, there were many towns founded on communalistic-Christian adherence. There were the German Lutherans in Iowa's Amana Colonies. There were the French Icarians (Catholic) who ended up settling Mormon-vacated Nauvoo. The biggest of all would have been Mormon migration to Utah orchestrated by Brigham Young, less than five years after Smith's death. Certainly, Smith could have exploited these same resources.
There was certainly room for a growing, prospering Nauvoo metropolitan area between Hancock County, Illinois and Lee County, Iowa. Today's St. Louis metro area has 2.8 million people. The State of Utah has 2.7 million people. Nauvoo can easily become a hub of water and railroad resources. After all, the then-navigable Des Moines River joins the Mississippi at the south end of Lee County.
I guess I am moving to a completely different thread: demographic changes if the Mormons remained here. So I will stop now.