That machinery was not available for decades later than 1860. The Southern planters would have continued to use millions of slaves to tend their crops and households. Once reliable tractors and crop harvesters became available around 1900, the planters would have shifted to their use. My point is that it would have been 40 years or more before slavery ended in the Confederacy.
Cotton production wasn't fully mechanized until the 1940s or even the 1950s.
Some of that long delay had to do with the lasting desolation brought by the Civil War and the poverty of the Great Depression of the 1930s, but there were serious technological difficulties involved.
One was the difficulty of removing the bolls that were ready for harvest without destroying the rest of the plant. Another was the problem of the mechanism clogging as it harvested more and more bolls.
There were all kinds of ideas for cotton harvesting mechanisms and many of them proved to be dead-ends. And having a captive labor force tended to discourage technological innovation.
If all went well for the CSA, you might have seen cotton production mechanized by the 1920s, but it could have taken a while longer, as it did in our timeline. You might have seen slavery abolished at some point after independence in favor of "neo-slavery" -- systems of control that weren't technically slavery but didn't allow much freedom to the agricultural workforce.