By 1865, 300,000 people in northern England were out of work due to the lack of Indian and Egyptian cotton vs. Southern cotton production.
Source
Consumer goods are far easier to target for boycott than industrial goods. Cotton was one of the lifebloods of the industrial revolution and throughout the 19th century, India and Egypt lacked the ability to meet that global demand. Ergo, the notion that Europe (or Northern US textile mills) would boycott slave-produced cotton is wishful thinking.
Setting that aside, and addressing the OP's question, the devil is in the details. The conditions by which a victorious CSA wins their independence matter a lot. A CSA that miraculously wins after the Democrats take back the White House in 1864 would be entirely different than one in which Antietam (1862) goes far more horribly wrong for the US. A late war victory for the CSA (however unlikely) would be one in which the CSA is forced to deal with a country in which slavery may exist on paper but in practice, it won't look very much like slavery of the antebellum South. Too much would have changed. I think a late war victory would result in something that looks more like apartheid long before 1900, simply out of their perceived necessity. Chattel slavery may get swapped out with peonage or wage slavery by the 1880s or 1890s or even earlier simply because by 1864 the social fabric of the South was already undergoing tremendous stress.
On the other hand, if the CSA somehow or another got lucky in 1861 or 1862 and captured Washington or the like, the institution of chattel slavery could have existed into the 20th century, because an early victory leaves most social structures intact as well as leaving most of the Southerners who died (
source) alive.
Although the CSA constitution explicitly supported slavery, it's worth asking the question, how easy would it have been to amend it?
Turns out, somewhat easier, in principle, than the US. The Confederate constitution required only three states to call a constitutional convention to amend their constitution. The US constitution required 2/3. Because of this, it is highly likely that if the CS Constitution wasn't working the way a majority of states wanted, a new constitution would have been voted on.
Something to think about, while the South was skeptical of northern industrialists, the later in the war victory comes, the more wedded to State-Capitalism the Confederacy became. Also, the more realization that their economy couldn't be tied to a single crop. A late war victory timeline that explores the growth of state-capitalism through the 20th century would be interesting.
There's not a lot that I like about Turtledove's TL-191 series, but one thing I think he nailed was that a CSA victory, regardless of when it came, would have doomed race relations in the North. Northerners would have been far more likely to have directed their bitterness toward freedmen and women than toward anyone else had the North lost, IMO.