Even if Jackson led the troops who assaulted Little Round Top that doesn't change the difficulties they faced when trying to capture it. They most likely still don't capture it even if Stonewall's leading them.
Note: Jackson's survival (and not being shot at all) does NOT mean he is attacking Little Round Top. Or Big Round Top. Or going around the Round Tops to the south. Or assaulting the Wheat Field, the Peach Orchard, and the Devil's Den. Or charging up Cemetery Ridge. Those were all for Longstreet's Corps.
Jackson's survival means that short of his having one of his rare lapses in judgement he will be the one commanding the attack from the north, at the wide open right flank of XI Corps. This is assuming that Jackson's aura doesn't change the minds of Buford, Reynolds, and Howard into making a fighting withdrawal to the south rather than a forlorn attempt to hold Seminary Ridge and the town of Gettysburg. Or else said aura doesn't cause a faster panic to make XI Corps run faster (and avoid a larger OTL-version entrapment).
But if indeed Jackson's
elan leads to the late afternoon/early-to-mid evening seizure of Cemetery Hill and Culps Hill, then Meade will have no choice BUT to fall back to the Pipe Creek Line, already under development at this point, and await Lee there.
And if Lee chooses to engage Meade there (he really has no choice, short of withdrawal back to Virginia), then history records a non-OTL Battle of the Pipe Creek Line that, for the ANV, look like the Battle of Nashville for the Army of Tennessee.