No, it isn't. Trading posts might work for a while, but the Brazilwood trade was very profitable, so much so that corsairs were a thing that Portuguese ships regularly had to deal with, a French corsair expedition is the whole reason Rio de Janeiro was founded
Brazilwood extraction is not enough to provide permanent and effective settlement. It necessitates very little infrastructure and military control when compared to plantations. Brazilwood colonies would be more akin to trade posts than actual colonies. France Antarctique was a different beast as it was a religious outpost first and an actual colony second, in the context of the French wars of religion. You are vastly underestimating the central importance of plantations to create complex societies and economies in virgin territory.
Eventually, a European power will settle down and colonize Brazil, after all, there's only so much wood you can find near a trading post before you have to go further inland to find more
How and what?
before gold is found and suddenly there's a gold rush which means more people will come to Brazil, it isn't too difficult to have serfdom appearing in the conditions after gold rush slows down too.
It took almost 200 years for gold to be found in Brazil. I don’t see why a less settled and economically complex Brazil would be able to find gold sooner. Also, don’t forget that the largest share of the workforce during the gold rush was slave labor. There was some Portuguese immigration to Brazil because of the discovery of gold, but this is the age of mercantilism. It’s not comparable to the gold rushes in the United States in the 19th century. Large scale gold extraction would still require slaves.
The Industrial Revolution will also be kickstarted earlier since people will want money-making to be less labour-intensive. I'd guess it would become popular somewhere around the 1770s-1800
Assuming it does start with no New World incomes and accumulation of capital, which is a big if (though granted, Potosi will still be there with or without the slave trade).
I'd also like to state that it is implausible for the Portuguese to hold onto Brazil, they will be the people who first discover it, but not the main colonizing power. that'd probably be France (Spain has enough shit, wouldn't really care about the Portuguese doing their thing and probably wouldn't risk a war with France over Guanabara Bay, England's too distant, and the Dutch don't have enough people to hold on to it. All whilst the French have enough people + interest in gaining more money, all whilst pissing off Spain which is even better). Mainly due to the fact that, as you said, plantations were the reason the Portuguese (just like any other European power) stayed, and without slaves that would be made more difficult. The French, however, have enough people (read: Protestants) to just put them on a ship going to Brazil, where they would work in the sugarcane plantations for a while before more people came in. It's not like Brazil's only purpose has to be resource extraction, it can be used as a base for French corsairs, expelling unruly people, pissing of Spain... The first two reasons would also contribute to making Brazil be a more settler colony (though not fully), which means there would be a significant demand to make sugar/coffee, mine gold + all kinds of hard labour that doesn't involve much skill, I bet my left nut newcomers would be both desperate and hopeful enough to do very intense work for the few first years if it means they get paid well, have a place to sleep and some connections when they truly start their new life, after all, if they aren't, other people will be.
It’s possible for the French to engage in Brazilian colonization, but then again OTL and their complete failure and later disinterest should not be discarded. It’s not like Brazil was a priority region of Portuguese colonization either. It only became a priority after the Restoration War and the loss of the East Indies. It’s not a given that a European power would colonize Brazil without returning incomes from cash crops. Brazil is hard to colonize due to its geography. Aside from being far from Europe, when compared to the Caribbean and North America, you have to consider vegetation such as tropical rainforests and first of all the coastal mountains, which I kid you not look like tropical Mordor when observed from the shore. A settler colony has little chance of working independently and, again, plantations cannot be sustained via indentured servitude. It did not work in the Caribbean, which is closer and smaller than Brazil, and it will not work in Brazil. It’s a matter of volume and of social tension. Slavery is needed to provide the required volume for the reproduction of the workforce and to create social cohesion among colonizers (what are you going to do with a bunch of landless white and Christian indentured servants once their plantation contracts are up and they start demanding land and employment?). There is no way that cash crops can work without slavery, at least not at the scale it is supposed to work with.
Convenience is irrelevant
Well, tell that to the user who actually brought this up, not me.
And, to be honest, Eric Williams, like most historians who dabble in economics, is not strong on his economics. They simply don't have a good grasp of the theory and the conceptual models. Being a good economist is all about having an intuitive understanding of which metrics are drivers and which are dependents, which are endogenous and which are exogenous. Economic historians love to take things like exchange rates and average rates of return as being fixed.
On the other hand, economists are not historians either. Applying economic models with no concern for the historical structure they are analyzing tends to also give distorted results. An excessively statistical and economicist history is more akin to speculative data rather than proper, methodical history. Naturally this also applies to Marxist historians.
Even if we ignore the fact he was a Trinidadian nationalist politician
He was a historian before he became a politician.
Even if we ignore the fact that the vast majority of capital for the industrial revolution came from domestic sources not the colonies
Controversial. Not only regarding Williams, but the entire Great Divergence field.
The reality is that diminishing marginal returns to capex combined with constant rates of depreciation mean that starting capital doesn't matter over the long term. If you have less capital to begin with, the net rate of return will be higher, if you have more capital, the net rate of return will be lower. This all nets out as being the same steady state of output for a given level of investment rate and technology. Read up on Swan-Solow if you really want to get up to speed on this.
Surprisingly I am familiar with the Solow model, though it’s not yet a model I’m 100% comfortable working with. I do know enough to think it’s not a very suitable model for pre-industrial economies, since it relies on concepts and structures that only really arose after the Industrial Revolution, e.g. if I am not mistaken salaried workforce that forms a bloc of consumers who demand goods from the capitalists. Then again, this isn’t really my field, like a pre-industrial Atlantic economy isn’t really Solow’s.
