There is much to suggest that had Stonewall Jackson not been killed in a freak accident the month before then the South would have stood a far better chance at Gettysburg. THe hill they were five minutes too slow in taking because Lee's orders were misunderstood; had they taken the hill then the fateful charge the following day wouldn't have happened.
I stopped at the part where Shelby Foote says that every Southern boy is able to put himself in that field at 1pm, just before the charge and drink in the last moment where victory was still possible.....I had to turn it off and weep like a baby..
That said, the situation at Vicksburg was dire and even victory at Gettysburg wasnt enough. He needed to draw Grant and his resources northwards to ensure that Vicksburg held and Gettysburg came too late- Vicksburg surrendered the following day.