Not to mention too that Joseph Smith's movement predates Miller by nearly a decade and a half.
Actually, a decade and a half would be even harder to believe -- simply because LDS is first, and therefore any butterflies emerging from it's lack of formation have a chance of disrupting the formation of the Millerites.
However, I think your equating the Great Disappointment with the beginning of the movement, which it isn't. Joseph Smith published the Book of Mormon in 1830. William Miller began his lectures in 1831. Both of them were in Upstate New York, but apparently not the same parts of it. This actually makes it more likely that they could have arose independently, since there isn't as much chance for effecting each other.
Both Joseph Smith and William Miller both were originally from around the same place in VT and grew up around the same place in upstate NY. They were both influenced by the charismatic, apocalyptic preachers of that area. They both came up with two vastly different religions. They probably saw each other as competitors rather than co-influential.
However... what about the OTL followers of LDS who don't follow LDS TTL? Do they just keep going about their daily lives, never to be heard from again, or do they decide to look into other religions? What does Brigham Young do? How about the children of the people who would have moved to Salt Lake City OTL? Could any of this have an effect on the growth of the Millerites? How about the lack of an LDS presence in Utah during the Civil War?
Brigham Young continues along as a traveling blacksmith ITL. He probably founds a successful blacksmithing chain, considering how charismatic he is.
Anyway, this probably would be a boon to the Bible Students. People who usually join movements like the LDS and the JWs and other charismatic religious sects who promise a much more fulfilling life, are usually disenchanted, down on their luck people. There still will be disenchanted, down on their luck people, and most likely, they'll join another charismatic evangelical religious sect. The Bible Student group would fit that perfect niche. The non-existence of the LDS church would have little or nothing to do with the Millerite movement, since again, they're from separate religious families.
I don't know if you haven't realized this by now, but the JWs and the LDSs are not the same faith, nor are they in the same family of denominations. LDS=Mormon family of churches, descended from the Baptist family of Churches. JWs/=Bible Student subfamily of churches, Adventist family of churches, descended from the Methodist family of churches. The JWs/Bible Students are about as different from from each other as the Black Southern Baptists and the Episcopalians. It would be akin to you suggesting that a sex scandal that involves the Archbishop of Canterbury would affect the Black Southern Baptist church. If anything, it would mean that the JWs get MORE members, since there isn't that much competition anymore for new followers. Cue the orange flying foxes from Beta Orionis 17.
And finally, only 400 LDSs participated in the American Civil War. I doubt the non-establishment of the LDS church would affect the civil war that much. If anything, Arizona Territory would have a few free counties up north, since slaves would have a negative economic output due to the lack of water and farmland in Utah.
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If the LDS church isn't established, the Millerites will still exist, but not have a west coast presence since the west coast is sparsely populated.
I think you're rather underestimating the influence of the Oregon Trail and the California Gold Rush in populating the West Coast.

(I'm assuming you mean the Rockies are more sparsely populated, which I could see).
I should have said "intermountain west" and not "west coast".
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Probably. The entire west was sparsely settled. Arizona and New Mexico didn't become states until 1912. A Mormon-less Utah would probably follow suit. A Mormonless Utah would push back the settlement of the west by 20 years.
That's a good point. Although, the difference between Arizona/New Mexico and Utah could also be attributed to things like: the proximity to California and Oregon Trails, a slightly wetter climate, a transcontinental railroad route, and proximity to the mineral deposits in the rockies. Some of these things could have happened differently as well, of course, especially the railroad route.
It's hard to say without working the timeline out very carefully.
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How about the state is named "Mojave" instead of "Deseret"?
The Mojave desert is southwest of Utah, mostly in California and Nevada. New Judea is more likely if a Bible Student-like group is naming it. However, I would expect that TTL will probably parallel OTL and have the government admit it as the state of Utah.
There's a piece of it that's located in SW Utah. However, seeing how the Bible Student group is iconoclastic, they'd probably name it "New Judea" rather than "Utah" or "Mojave", since they're both references to ethnic groups.
Where I'm having the most difficulty seeing this, though, is the period of time between Miller beginning his speaking in 1831 and Russel beginning his work in the 1870's... or rather, the path between Millerism to Adventism to Bible Student Movement in a world with a a huge LDS vacuum.
None really. If anything, Miller would get more followers since there was no LDS church to compete with.
While I could easily see something *similar* to the Bible Student Movement emerging, maybe even begun by someone named Charles Russel, I have problems seeing it looking exactly alike, and therefore probably not leading to the same sort of schism.
The Adventist movement is rife with schisms (7th Day, Second Day, Bible Students/JWs) so a home church movement started by a disaffected Adventist would be an inevitability.