If we're going to get pedantic, it's more accurate to say that both the Kingdoms of Spain and Portugal were dynastic possessions of the House of Hapsburg from 1580 to 1640. Hence why it's called a "joint monarchy" or "personal union" in English - Portugal was never folded into Spanish state control, it was just another hereditary claim of the Kings of Spain, like the Low Countries or Naples.
In terms of real-world impact in South America, based on the sources I've looked at, the joint monarchy was pretty negligible. Brazil was in many ways an independent state long before it actually split off from the Portuguese empire, anyway.
One of the triggering events for the independence of Brazil
was a 13 year period during the Napoleonic wars when the
Portuguese Crown and their court of ~15k people moved to Brazil just before Lisbon was invaded.
