I disagree with that.
Had Lee's invasion of the north been successful disHonest Abe would have pulled troops out of the west to try to repel the South. (Actually, Newt Gingrich exploits this very theory in the third of his WBTS books, Grant Comes East.)
Also, Gettysburg was not a rout by the north. Had Stuart been there from the beginning, Lee would have been able to complete his mission, which was to push to Harrisburg, Pennsylvania, or even Philadelphia, to influence northern politicians to give up their prosecution of the war.
Stuart was where Lee sent him. Moving along the Susquehanna to rendezvous with Ewell, who was ordered to capture Harrisburg.
‘Had Lee’s invasion of the north been successful ....’
Define ‘successful’.
Lee wanted a single battle to decide the war. It was his training to think in such terms.
The problem is warfare had changed dramatically, as we know in 20/20 hindsight. At Gettysburg, Lee had no chance at all of obtaining such a victory, even if the Union had collapsed on the evening of July 1st, or if Longstreets attack on the Union left had been successful on July 2nd.
Picketts Charge? Same problem with the first two days worth of attacks. Even if he had taken the Union Center, there still wouldn’t be a situation as a result giving Lee what he knew he had to have, the utter destruction of the Army of the Potomac.
Its easy to see why this is so, by looking at the map. The Union not only had the obvious advantage of the better ground to defend, they also had the network of roads to withdraw down towards DC and its stunning fortifications.
Next, Lee’s army was one of manuevur, not of seige, nor of occupation. Engaging in warfare in urban settings, he would have been at a distinct disadvantage, which is why I always shake my head at suggestions he could have taken Philadelphia or New York - let alone deal with the supply problems that type of action would have brought about.