...and in the end, it wouldn't have mattered, as the war was to be won or lost in the east. By 1865, the troops in the west would be cut off, and the Union could crush them at their leisure.
By the time of the ACW, the Mormon problem was largely irrelevant. Tensions had eased off greatly before Lincoln came to office... and when he did become President and was asked what he intended to do about the 'Mormon problem', Lincoln said flat out he was going to leave them alone. I doubt the Mormons would abandon this for the uncertainties of joining the lost cause of the CSA... for that matter, I find it unlikely that the rather arrogant CSA government would like the Mormons all that much.
Interestingly, the troops the CSA had west of the Mississippi were the last ones to surrender.....