I believe that it was possible but it would have required a change of tactics that would have been dishonorable in the minds of most of the military leaders of the day. It would have required the intentional destruction of forces of the North. Not just winning battles, but the willful and deliberate pursuit and killing of retreating forces.
Be careful what you wish for, because many times behaving as a ‘monster’ only creates a bigger ‘monster’ and if the South didn’t suffer enough as it was after losing just imagine what would have happened if they lost after using such tactics.
Civil war battles often left the winning side just as beat-up and battered as the losing side. The fact is that often the winner couldn't pursue. Or if he did pursue, as Meade did do after Gettysburg, it was with only part of his force. Lee fought a very skillful rear guard campaign all the way back to Virginia. Meade didn't pursue as well as he could have, but he was putting his army back together.
I think you’re onto something here. The only way I can see for the Confederacy to have won the war is to do something like the guerilla war that the North Vietnamese used against the French and later US forces in Indochina. That type of fighting was certainly considered to be dishonorable by all parties concerned during that time, though, so it’s unlikely that the Confederacy would have resorted to all-out guerilla warfare.