I don't think goldfinger's argument works, for a couple of reasons. The argument seems to be three-fold: slavery is necessary to create the raw material for industrialization; slavery is necessary to create the capital for industrialization; slavery is necessary to get the human beings in place (both as laborers and consumers in the colonies) for industrialization.
I described above why I think that's not accurate about capital. It's not like people were putting the money they made from sugar plantations directly into textile mills, and it's not like colonial income alone entirely changed the fortunes of the English economy. Doubtlessly a richer England was better suited to industrialization, and colonial ventures founded in part by slavery related to that, but I would argue that it's not necessary for industrialization and could in fact be harmful: in the long run, Spain got poorer, not richer, because of its slave-based colonies. England was the least effective colonizer of the 1500s and 1600s, and ended up the richest. That is not coincidental.
It also doesn't appear to be correct, or at least not entirely correct, with regard to the production of agricultural raw materials. I'm not as familiar with the situation in the Caribbean or South America, but, it's certain that American agriculture could be just as successful without slavery [Santa above accurate points out that the relative profitability of slavery to free labor, in the South, was in the big picture beside the point]. We know this, because American agriculture was just as successful without slavery. Production didn't collapse because slavery ended; it took a while to get recovered from the worst war in American history, but by 1879 (the earliest number I could find in a couple of minutes of Googling) American cotton production was above pre-Civil War levels. In fact, the USA was quickly to the point where farmers produced too much for prices to stay high, even before the end of the 19th century. Some of this is because of innovations associated with industrialization, like chemical fertilizers, but it still indicates that slavery is not a crucial ingredient (at least in the United States) for massive agricultural output and therefore industrialization.
Thirdly, slavery is not necessary for laborers or consumers in the New World. In fact, it's antithetical to them: the highest levels of free immigration happen in those places where there's a large demand for free labor. The South by and large was not a destination for immigrants coming to the USA, unless they had chains on, until well after slavery ended. It's clear that free laborers would produce cotton (again, they actually did), and likely a free labor system would have produced even more -- any gains lost with the removal of coercion as a tool would have been gained by the incentives of profit. The southern slave system made three kinds of people very rich: the merchants trading the raw material, the industrialists turning it into finished goods, and the plantation owners. You can have the first two, and the associated capital etc for industrialization, without the last. It's possible it would have taken slightly longer for the South to get populated, but, once it started, it would have gone even faster than it actually did. And, since we are considering consumption as well, free laborers provide a better market for finished consumer goods than do slaves. It's not like plantation owners were buying lots of nice clothes for their slaves.
Finally, let's recall the point of this argument. The idea is that the whole world would be so much poorer without slavery that Africans, who have had much of their continent ruined by slavery and associated evils, would be even worse off without the slave trade. Even if industrialization had happened later or less fully (which, as described above, I think is the opposite of what would have actually happened without the slave trade), Africa would still be better off economically.