But tell the whole story to why they still have wishy-washy economies that constantly contract that's backed by excessive centralism that birthed class hegemony, abnormal illiteracy, social inequality, sustained low real incomes and enormous poverty rates. This all stems from slavery and the subsequent failure to invest human capital through education and social reform.
Who cares if those countries industrialized, they didn't put any of it to good use and it only benefited a few people and they still have a weak government structure. The probability that the south would have followed that pattern is rather strong because it appears they had no intentions on freeing the slaves anytime soon and their Jim Crow laws indicate they had no interest in investing in class equality, education and social reform. All the evidence points in the direction that the south could have emulated SA and Brazil's so-called sophisticated industrialism is not much to brag about.
Comparing the British and US industrialism to other countries industrialism is rather dull and a bad comparison because of the education rates were much higher. The inventions, technology innovations and education systems compelled the north to an economic expansion during the Gilded Age that was unprecedented. It had more to do with just industrializing and how it became industrial , it had to do with masses of the educated people who became engineers, scientists and entrepreneurs which built a core country.
From 1776-1860, 93% of the major inventions from in this country were from the free states. The literacy rates were like 75-80% in the north, whereas 7% inventions and 50% were illiterate in the south while they held onto slavery.
Yes, the south would have had the same outcome as Brazil and SA.