Could the Confederacy have maintained slavery even after the civil war was underway?

Yes. Parts of the Confederacy did.

They seceded, 11 of 13 to be exact. They said they were no longer part of "The United States" and they continued with their way of life which included the keeping of slaves and slave labor.

They didn't think it was wrong when they were part of it and sure as heck didn't think it wrong when they had seceded.

At least until Lincoln came out with his Emancipation Proclamation. And even then some slave owners - most plantations were destroyed by the Civil War - did not follow it. A few did though