Unfortunately, I do not think the Native Americans would get more than a few years respite from contact with Europeans. In our timeline, a Portuguese fleet intending to sail off course drifted west to make landfall in Brazil. That voyage occurred independent of Columbus and there is no reason to think it would not serve as the first contact in this scenario. Now, what does that mean for future voyages and eventual European colonization?
Who explored what in our timeline was initially very random, and there is no reason to think there might be any sort of predictable pattern to the voyages of this alternate universe. One important early alteration, however, is the absence of a Treaty of Tordesillas, which effectively bottled up the Portuguese in Brazil to the benefit of the Spanish. In this scenario there is no reason to think the Aterni Regis, the 1481 Papal Bull which affirmed the Canary Islands as Spanish territory and granted all land south of them to Portugal. That means all the riches of Central and South America are nominal Portuguese, at least in the beginning.
How long the Portuguese could hold to such immense treasure is another question. In 1580, a Portuguese succession crisis resulted in the King of Spain seizing the Portuguese crown, effectively uniting the two lands. I suspect such an event would occur early, if possible, and that Spain would be more invested in holding onto the Portuguese crown for as long as it meant owning the riches of the Incans and Aztecs. Though the question must be asked, would there be Portuguese equivalents of conquistadors in this timeline?
I have to say no. Portuguese history during this time period shows much more interest in establishing trading outposts in foreign lands to trade with locals then in conquering large swathes of territory. Thus the Native Americans have gained valuable time, perhaps as much as century, to regroup from inevitable decimation by disease and mount a defense against whatever Europeans might try to steal their land.
Whether an analogous situation to Africa is possible, where the native people survive European colonization and eventually throw off the foreign masters, is debatable. It should certainly be possible in the more densely populated parts of Central and South America, though I am more skeptical that European land-grabs could be resisted in North America, particularly if that is Spain'smain theatre of operation early on. Speaking of Africa, the lack of an African slave trade that a stable native population would assume will have massive implications on West Africa's history.
I won't try and cover all of the butterflies in this one blog post. If you are interested in reading more, read this thread on alternatehistory.com, where I contributed to a collaborative timeline based on this very concept.
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Sorry for the late update, life has been a little hectic. I can just about guarantee I will be off schedule this coming week, with Easter and all. But hopefully I'll be able to fall into a nice pattern at some point. And remember, if you like these articles, share them!