I normally don't like to sandbag the POD, but this is extremely unlikely to happen.
1) The raising of black troops would be extremely divisive within the Confederacy. Too many of the political elites would be against it. A large part of the White enlisted men and officers might just go home.
2) Why would any of the black slaves in the Confederacy join the CSA at this point in time (honestly, at any point at all)? The North has already made abolition of slavery in the South as one its de facto war aims with the Emancipation Proclamation. While the Union is stymied in Virginia, it is trouncing the Confederacy in the West. A lot of the black population is already aiding the Union war effort in one way or another - outright flight to the Union armies, service in the Union armies, acting as guides or informers, and probably a not insignificant amount of work slow downs and sabotage. It is hard to see any kind of appeal that would cause a significant number of black slaves to enlist.
3) Black Confederates are likely to highly unreliable in battle, and not trusted by their white commanders. What Confederate general is going to use them in battle? Put them in a critical part of the battlefield? Or simply trust them not to defect to the Union the moment the Union forces come into contact?
4) Considering how badly the Confederate economy is, what happens when most of its available labor manpower is now taken away from it? Who is going to do all that work?
If some strange bizarre reason this did work, and it was able to reverse the Confederate defeat, you have the situation where there are large numbers of black Confederates who are now free, have training in arms, and have weapons. This is a recipe for massive political instability. Potential for a mass slave revolt is ripe. Even if it is defeated, it'll put even more strain on a society that just ended a very long and debilitating war.
There will also be additional political instability among the fire eaters who feel completely betrayed by the calling up of black soldiers. There is going to be fierce divisions within the Confederacy.
Even if by some miracle this plan worked, the lifespan of the CSA as we know it is likely to be only a few more years before it enters another war or have many states secede from it, or just have the authority of the CSA collapse within certain states.