I think the answer would have been "Yes" the battle would have been different. I think Jackson would have taken Culp Hill on the first day and held the line and maybe moved on toward Cemetery Ridge.
The second factor would have been that Lee would have been more aggressive than he was. He would have allowed A.P. Hill's leading men to not just seek out the town and not force a general engagement. This pause caused the Union army to gain a solid foothold on Cemetery Ridge. Well... Buford and Reynolds doing a great job of falling back.
Third factor I think, is the entire campaign would have been different. Lee plans would have been conversed and analyze with Jackson as him trusting him for insight. You have to remember this was the first time Lee was going about leading two new Corp commanders, A.P. Hill, and Richard Ewell. Lee wasn't all that sure of their command, he respected them both and admired their qualities but to see them handle themselves as Corp commanders in battle that was the unknown to him.
Lee would have acted braver, more decisive, and more aggressive with Jackson at his side. I do not think "just" Jackson would have made the difference it goes beyond just what his troops could have accomplished but rather how Lee was to orchestrate this campaign with his trusted Jackson, that would have made a difference.