That is hard to say, the ruling elites certainly had a vested interest in keeping the institution of slavery going however slavery depressed wages for poor whites. My best guess slavery would have ended in the CSA by the 1900’s. With the black being returned to Africa in most cases.
Had the south seceded they would have been able to sell their cotton without the onerous tariffs. They wouldn’t be forced to sell their cotton cheap to the north. Slavery would have ended soon.
The real question is: How long could the northern textile mills last without the cheap cotton extorted from the south? Not long.