Illinois would possibly be a swing state if we assume no Mormon migration, as I believe there are some areas there that Mormons consider their 'holy land.'
Close but no cigar. (Of course Mormons don't want cigars.) Nauvoo, Illinois is important but Independence, Missouri is the location of where the City of Zion will be in the last days. Kirtland, Ohio is also of some importance as the site of Joseph Smith's first temple. Incidentally, the temple properties in Kirtland and Independence are not owned by the Mormons but by a different branch of the LDS movement, the Community of Christ. CoC is the branch that considered Joseph Smith III instead of Brigham Young to be Joseph Smith Jr's successor and is the second largest LDS church.
My mother's family is CoC so I was more or less raised in that church for several years. A couple of my mom's siblings even worked as tour guides at the Kirtland and Independence temples some summers as college students (my mom was never terribly devout).
I tend to think that had the mass exodus to "Deseret" (Utah) never happened, the Mormons would look more like Community of Christ does today - much smaller, without the distinct culture. CoC at this point is basically a mainline Protestant denomination. They consider themselves a "peace church" and aren't particularly dogmatic on cultural issues like abortion and homosexuality. The congregation my family attended did not even use the Book of Mormon - it was in the pews next to The Bible and the hymnals but sermons never incorporated it and we were never taught about it in Sunday School. I think part of the reason for this is that unlike the LDS church, CoC members were always a minority in predominantly Protestant areas and thus adapted and evolved to avoid the discrimination Mormons had suffered earlier.