No, because it's a false premise.
Why? The Soviet Union industrialized in part because of slave labour used to build the industrial capacity of the nation. Do we not discount this when we measure the economic performance of the USSR or do we whitewash it and say it doesn't matter?
The insinuation being that the north did not have slaves post 1861. Law was written, sure. But they were gradual measures. Furthermore, northern states certinaly did not extend the franchise to blacks post abolition.
That's true but it misses the point. This isn't about racism or voting. It's about the economy. In 1860, the South's economy was based upon agriculture, which was reliant almost entirely on slave labour. The north was industrializing, which was dependent upon wage labour. The vast majority of labour in the North at the time of the Civil War was based on wages.
So to ask for all people or white people from a standard of living context of the south is moot. As Bro said, the south had a very wealthy culture following the cotton boom. The north, being more industrialized, (contrary to other assertions) saw standards of living in shambles. Textiles being the obvious go-to as a point of reference...or shall we say, sweat shops.
I took a full year honours course in economic history of North America in college 20+ years ago, and I recall that the standard of living in the South as not being anywhere near the standards of living as the North. However, I cannot find my old textbook so I can't confirm that. So I might be wrong. However, I did find this from Gavin Wright entitled
Slavery and American Economic Development
"Contrary to depictions off the slave South as a propserous economy devastated by war and abolition, these essays locate the root of postebellum regional backwardness firmly in the antebellum era. That era was indeed propserous for the slaveowners. But if we evaluate regional performance using a consistent measuring rod appropriate for a free society, such as the value of nonslave wealth per capita, we find levels in the South just over half those of in the free states."
Also, the idea that an agrarian society was generally wealthier than an industrialized society contradicts economic history to this day. The progress of economic history throughout the world has followed a similar pattern:
agriculture --> manufacturing --> knowledge base.
Agriculture generally is subsumed by manufacturing because manufacturing is higher value-added, which requires higher productivity, which means higher wages. Historically, workers flock from the farm to the city to work in manufacturing because they can earn a better living. This happened in Europe and the UK, it happened in America, it happened in the Asian Tigers, and is happening in China today. That the South was somehow immune from this pattern and different smacks more of historical revisionism designed to reinforce confirmation bias of those in the South.
It also reinforces the Marxist argument that American capitalism was built on slave labour. In fact, our understanding of economic progress and the critical importance of productivity in the development of capitalism contradicts the argument that the South was a richer society, or at least would remain so. Economic wealth is driven primarily by productivity growth, not by slave labour as the Marxists claim. We empirically know that productivity is the driver of higher wages and returns on capital, and thus drives economic growth. Slavery reinforces the discredited Marxist theory of The Surplus Value of Labour. It's odd that self-proclaimed libertarians cling to this notion of the Confederacy being richer than an industrializing society.
But again, maybe I'm wrong. Feel free to show that I am.