What if Lee does not engage the North in Gettysburg, instead opting to penetrate deeper into the North? How long until he eiather out-runs his supplies or is caught? How does this affect the North? The South?
I don't think it was willingly that he engaged there. There are some stories that they were after a shoe factory in town to requisition and it caused a general engagement because of a lack of discipline from advance units.
But the truth is that if they did not engage at Gettysburg, it is possible with the pace that the Union Army was moving that his forces would have been caught and engaged piecemeal somewhere on the road from Chambersburg towards the bridge all the way up at Harrisburg due to the negligence of the Confederate cavalry in the campaign.
This could have gone very badly for Lee. I think that his skill would allow him to extricate his army, but if he doesn't engage at Gettysburg, and manage to get pretty damn lucky knocking out two Union Corps merely because of the order of march that sent a massive amount of troops onto the Union flank by chance, his army could be in serious trouble, especially if the force does not consolidate quickly enough.