I've never really bought that story, in that form. It tacitly suggests that the South's economy was stronger with slavery than without. It seems more likely to me, though, that reliance on slavery was part of why the South's economy ended up being so weak in the first place. It allowed money to remain concentrated in the hands of a small, landed elite. That worked out extremely well for them relative to their neighbors, but also would have fueled a sort of falling tide that sinks all boats.

Which isn't to say that it doesn't change the economic equation if you take it away. But it's more tenable to say that the reason people were willing to go to war over it was more about the economics of power than about economics in general.