The current question is not whether or not Jackson, having survived his wounds or not been shot, would have performed better at Gettysburg than A.P.Hill, Richard S. Ewell and James Longstreet combined but whether or not Gettysburg would have been fought.
It is generally believed, by those of us who have been arguing about the ACW for a long time, that Jackson would do one of two things.
The first thing he might have done would be to push his forces harder than Ewell did on the first and and taken the risk of capturing the heights before Union reinforcements could arrive. In this scenario the idea is for Jackson to be able to gain the height and hold his positions againt the Union forces until Confedeate reinforcements could arrive to reinforce him and consolidate the Confederate positions on the heights.
There are difficulties in this scenario. For a start the streets in the town of Gettysburg that the Confederates woulf have to march through to reach the height were narrow and would leave the Confederates exposed. Another difficulty would be that the Confederate soldiers would be exhaused by this time. Also more Union troups are arriving so it would be hard to take the hill and hold it. Culp's Hill could be captured on the first day, making the Union positions on Cemetary Hill unatainable, but whether or not it could be held long enough to consolidate the Confederate positions is debatable
The other scenario which seems would be likely is that Jackson would take the same stance as Longstreet and he would regard Gettysburg as unfit for battle and would favor withdrawal from the North toward Virginia where the ANV could dictate where the next battle would be fought and would be able to rout the AOTP once again.
For such a scenario, where the ANV has avoided any major loss of life, I believe that, following a withdrawal south, Lee would be prepared to make movements towards Washington, though it is unlikely he would ever be able to capture the capital at this point in time.