Disorganized and equally tired. Before you can really chase a routed army you must be able to have supply lines that can sustain it. You also have the chance to run into a fresh army that was coming to support the other. Don't forget that many of these men had to walk great distances to end up fighting at the end of the day.
Unequivocal NO. Had Abraham Lincoln lived, it may have. When he died, so died the spirit of reconciliation. The following decades were filled with exploitation and abuse of the local population from the carpetbaggers and their imposed power/governance.
If your wanting to know of the capture of New Orleans in 1862 then the Union won
otherwise....During the War of 1812, despite the Treaty of Ghent already being signed, the US Army took the field and won the battle under General Andrew Jackson. This was because after the treaty was signed it took many month for someone to travel to new Orleans and tell them the treaty was signed.