The problem is timing. The Mormons needed a place to settle before 1850. It took twentieth century shipping and technology to develop any significant settlement on the south coast of Alaska. So to get there, the settlers would have to travel all the way to the Pacific and board ship to travel north. In OTL, they had a well-traveled trail that became the course for the transcontinental railroad in 1869, providing a modern conduit for settlers. Now, to their credit the Mormons did attract hard-working and creative people who could make advances in intensive farming, greenhouses, fish harvests, coal mining, etc. But they would need a good way to move people and raw materials in, and manufactured goods or packaged seafood out. That might work in the 20th century, but it is questionable in the 19th.