If it's like OTLs pandemic, it's going to fall hard on both armies, though probably harder on the Confederate Army since they weren't as well fed or clothed. The war could grind to a halt until the pandemic passes.
Of course, this could also affect the French Invasion of Mexico, the Meiji Restoration, the Taiping Rebellion, German Unification, and Italian Unification.
Plus, a lot depends on who falls ill and whether they survive. The right person dying could trigger any number of succession crises - for just one example, Napoleon III's son is still a child. If Bismark dies Germany will not unify the way it did. Other single deaths could erase the Bahai religion, or acceptance of the doctrines of the Immaculate Conception and Papal Infallibility, or the Nobel Prize, or the Suez Canal.