Did they? I somehow doubt that. I'll give you they have crop, and whiskey. They also have a way to sell to gain funds. At the same time, I don't see them getting any significant quantities of glass, copper, nitrates, and several others if disconnected from the port cities. For example, around this time, New England could survive with a total block on the rest of the world... but most of the population would be reduced to a 15th century living standard.
Illicit trade and smuggling would still occur though. Also, the Boers didn't reduce to a 15th century living standard.
Also some of the urban artisans/craftsmen/blacksmiths would have been former "Patriots" in the revolution, and some emigres may join the existing farmers if there is significant cultural and political pressure against former rebels.
My point was mainly that they had a population, not that their economy would be perfect, but I think they wouldn't lose any technology.
This is going to sound very Draka like but what about the Cape. Owned by the Dutch who were opposed to the British in the war, fair climate and slave owning.
Texas is another option but maybe too close to the British?
The
states colonies whose economy were most heavily based on slavery were Loyalist though. Actually, I would not be surprised if a British victory in the ARW leads to the British supporting slavery for decades longer due to it playing a larger part in the Empire's revenues.
So while these "American Boers" may not be strictly abolitionist, they aren't, for the most part, going to be plantation owners. They will be smallholding farmers. There would be plantation owners joining them in the following decades as cotton cultivation expands, but the founding "pseudo-Boers" generally won't belong to the elite classes of Georgia, South Carolina, North Carolina, and Virginia.
edit: Although some of the OTL Founding Fathers from Virginia might go west.