Not so much when you properly account for the enslaved population. It's just not sensible to only count free citizens, that's clearly a misleading impression.
It is not a misleading impression, the south as a territory was fairly wealthy for much the same reason that todays California is fairly wealthy, that does not mean that the wealth distribution was good, nor does it mean that I advocate for a return to that system as it was abhorrible. The south was a shining example of wealth concentration and the ability to control that it brings. But economically it was strong, so strong that they had a slogan that cotton was king. The implication was that the European powers and their need for the souths exports would drag them into the war on the souths side. It was prides folly to think ]their economic hand was that strong, and they certainly overplayed it, but it was strong and that is why they felt they could play it.
Its worse than that, its not about not counting the slaves, the slaves literally are the wealth they were counting, and were the largest capital asset in the country.