It was absolutely economically viable. In fact, Southern plantation owners were amongst the richest people in the world.

Very many plantation owners could sell around $50,000 worth of cotton to the market per year. Contrast that to the salary of a poor white southern man, about $150 per year.

Labour was “free” if the plantation owner inherited the slaves. (It was extremely expensive to buy into the situation. ).

Income could also be derived from selling off slave families and children from northern slave states to the Southern slave states. An average slave was worth about $1,000. A female who bore 7 children created an asset worth $7,000. A massive sum of money.

When you say “Market Revolution”, were you thinking about a manufacturing revolution? The cotton gin, free trade, fast ships, cotton mills in England, financial services in New York were all advances in capitalism and manufacturing which promoted slavery and helped it grow.

In summary, slavery was quite strong and “healthy” when the institution came at a crossroads in 1861.

Matthew Karp's This Great Southern Republic is a fantastic read at several levels and addresses part of this. While it's dedicated to how southerners were determined to preserve the U.S. as a bastion of slavery and did manage to drive the helm of foreign policy for a time in the 1840s, part of it was also their firm belief that slavery was the economic mode best suited to their way of life. They formed journals and publications designed to push the idea that free labor would never be able to produce cotton on the scale that industry needed, and that the British could only do so by compelling cheap labor to work on their behalf in India and Egypt.

I suppose the answer to whether it was economically viable depends on what perspective you're looking at. It helped push the South into monocrop dependency that could lead to frightening to boom-and-bust cycles, but that process intensified after the Civil War if anything: read Steven Hahn's Roots of Southern Populism, and he points out that the percentage of land devoted solely to cotton production increased dramatically after the war. Was it successful for the slaveholders? Absolutely. They were frequently heavily in debt as well, but they enjoyed incredible standards of living. The South was well integrated into a global economy in 1861, so I think it's safe to say capitalism and slavery could easily coexist with each other.

Follow up: What was the effect this 1820-1850 American slavery had on poor whites in the South? Did slavery stop the free labor ideology from spreading from northern whites to southern whites?