He got there in time for the finale and his services by then would have been minimal at best.  Lee nearly won the battle on the second day, but Chamberlain held the line ferociously.  Lee was suffering from battle fatigue and so he erroneously thought he could smash through the heavily fortified center.  Had he listened to Longstreet and attacked at one of the flanks again, he might have knocked the Union troops off of Roundtop and carried the day.  Gettysburg would then have been just another Confederate victory, but it would not have done more than lengthen the war in the Eastern Theater….and possibly caused Lincoln to lose the election to Clement Vallandingham.  Vicksburg would still have fallen though and the end result would have been the same.  Vicksburg was the more important victory in terms of military strategy.

One reason for Stuart's inability to supply Lee with intelligence on Union movements was the dramatic improvement of the Union cavalry.  They hounded him and prevented him from gathering info and getting back to Lee in time.  I have been told that the invasion of PA by Lee was a diversion to try to draw Union forces from Vicksburg.

If I recall, Jefferson Davis was hoping that General Kirby Smith could dispatch Richard Taylor from the West Bank of the Mississippi to somehow relieve Pemberton at Vicksburg, but Taylor could barely muster a brigade as a token gesture.  The Confederates really didn't have logistical support from any direction once Johnston was driven back at Jackson and thus prevented from joining up with Pemberton's forces.  Pemberton should have abandoned Vicksburg earlier and saved his 22,000 men, but he did tie down tens of thousands of Union forces because Grant initially couldn't figure out a way to penetrate the tight Confederate defenses…until Porter secured the river.  To Grant's defense though, he did learn some very important things at Vicksburg that later helped him in the Virginia Theater.

His victory there also got him his job back east.  Wasn't Johnston criticized for being painfully slow in getting to Vicksburg?

Johnston was criticized for a multitude of things including not saving Vicksburg, but the reality of the situation was he was not strong enough to break through the Union forces besieging Vicksburg.  My personal opinion of Johnston was he was no fool and usually did the prudent thing with his army.  Pemberton was more at fault for not evacuating when he had the chance.

If I recall Grant had anywhere between 60,000-80,000 at any given time with 20,000-40,000 in reserve anytime he needed them in Tennessee and Kentucky.  Vicksburg was a very difficult place to assault and Grant pretty much figured this out when his multiple attempts failed miserably…but he took notes on what worked and what didn't.  He wasn't afraid to try and this was the one quality that Lincoln saw in the man.  Grant failed at many personal ventures in his life, but he was never afraid to try something new.  Though he was a failure in the private sector, his persistence paid off in the military sector….especially when so many of his comrades were complete idiots like Pope and Halleck or Burnside even.  Grant was truly a diamond in the rough for Lincoln.