I think a bigger wild card is the population of the South losing its will. Privations were greater down south. The Union armies were down south. The political leadership was more fractuous and less competent down south. Absent an immediate collapse of U.S. morale, and there is no reason to think that yet another battlefield defeat would do that especially with the victory at Vicksburg, the U.S. would have continued and the Confederacy would have been defeated.
Have you ever read “Guns of the South” by Harry Turtledove. Fascinating read and the only book of his I REALLY like.
I've read a bunch of his stuff, but not that one. I'll have to look it up.
Most of his others annoyed me because they were stringing me along. That one is different. A bunch of German South African racists from the year 2013 (IIRC) supply Lee with 100,000 AK47’s - and training to use them - shortly after Gettysburg. The results and details are very interesting