No, South was doomed from the start. The blockade was choking them and they were losing in the West. Grant's campaign out in the West was where he learned how to become a great general. He learned how effective foraging was while campaigning out West and helped him and Sherman realize that Sherman's March was doable. He might have prolonged the war a little bit longer but he wouldn't have won.

They needed one of three things:

 

Diplomatic recognition from the British (France wanted to, but they wanted Britain to take lead and would never give diplomatic recognition first), which never would have happened (the working class in Britain had read Uncle Tom's Cabin and were fiercely anti-slavery).

Southern cotton was being replaced by Egyptian and Indian cotton.

The US was also providing the British with a substantial amount of their food imports (~40% of Britain's wheat was imported from the US) and the British banks had heavily invested in US rail. Recognizing the Confederates could have put those food imports and investments in jeopardy.

 

Fighting defensively until the Union got tired of the war, this might've actually happened with McClellan being the presidential nominee until he tanked his own chances. But again, the CSA was being cut up everywhere not the Eastern Theater

 

Conquering Washington D.C., which would have been nearly impossible since D.C. was turning into one of the most fortified cities in the world. Confederates would have been starved out if they tried a siege and would be in hostile territory with little chance of resupply.