Sir William Hawkins, an English businessman, ship's captain, father to William and Admiral Sir John Hawkins, Mayor of Plymouth, and Member of Parliament, made several voyages to Brazil. He is thought to be one of, if not the first, voyagers to complete the triangular England-->Africa-->South America-->England journey. On one of these voyages, he brought a native "King" to the court of Henry VIII, as noted in his son, Admiral Sir John Hawkins', writings:
"Old Master William Hawkins of Plymouth, a man for his wisdom, valour, experience and skill in sea causes much esteemed, and beloved of King Henry VIII, and being one of the principal sea captains in the West parts of England in his time, not contented with the short voyages commonly then made only to the known coasts of Europe, armed out a tall and goodly ship of his own of the burden of 250 tons, called the Paul of Plymouth, wherewith he made three long and famous voyages unto the coast of Brazil, a thing in those days very rare, especially to our nation. In the course of which voyages he touched at the River of Sestos upon the coast of Guinea, where he trafficked with the negros and took of them elephants' teeth and other commodities which the place yieldeth. And so arriving on the coast of Brazil, he used there such discretion and behaved himself so wisely with those savage people that he grew into great familiarity and friendship with them. Insomuch that in his second voyage one of the savage kings of the country of Brazil was contented to take ship with him, and to be transported hither into England: whereunto Master Hawkins agreed, leaving behind in the country as a pledge for his safety and return again one Martin Cockeram of Plymouth. This Brazilian King, being arrived, was brought up to London and presented to King Henry VIII, lying as then at Whitehall: at the sight of whom the King and all the nobility did not a little marvel, and not without cause; for in his cheeks were holes made according to their savage manner, and therein small bones were planted standing an inch out from the said holes, which in his own country was reputed for a great bravery. He had also another hole in his nether lip wherein was set a precious stone about the bigness of a pea. All his apparel, behaviour and gesture were very strange to the beholders.
Having remained here the space almost of a whole year, and the King with his sight fully satisfied, Master Hawkins, according to his promise and appointment, purposed to convey him again into his country: but it fell out in the way that by change of air and alteration of diet the said savage King died at sea, which was feared would turn to the loss of the life of Martin Cockeram, his pledge. Nevertheless the savages, being fully persuaded of the honest dealing of our men with their Prince, restored again the said pledge without any harm to him or any man of the company: which pledge of theirs they brought home again into England, with their ship freighted and furnished with the commodities of the country. Which Martin Cockeram, by the witness of Sir John Hawkins, being an officer in the town of Plymouth, was living within these few years."
Edit: clarification
I can't help you with the Conquistador era, but I do know that in the nineteenth century, many European explorers to the Southern Cone brought indigenous men and women back to Europe with them. One famous example is that of Orundellico (commonly known as Jemmy Button), a Yámana man native to Tierra del Fuego who traveled to Europe in the 1830s. He actually traveled aboard the HMS Beagle, which is the boat that Darwin would later take to Patagonia. Several years after his return to his homeland, Button, carried out a massacre against missionaries in Tierra del Fuego, despite the fact that many Europeans thought he had been 'civilized' during his time in Europe. For more info, see Ruth Mayer, "The Things of Civilization, the Matters of Empire: Representing Jemmy Button," New Literary History 39:2, 2008.
In the 1870s and 1880s, European sailors, explorers, and anthropologists from a number of different countries (incl. France, Norway, and Germany) took indigenous people from Patagonia captive and brought them to Europe to be displayed at ethnographic 'zoos.' If you read Spanish, there is a book called Zoológicos humanos: fotografías de fueguinos y mapuche en el Jardín d'acclimation en París, siglo XIX by Christian A. Baez that gives information on several indigenous individuals and families who were put on display in Paris as anthropological subjects.
Again, I'm not sure if this is the era that you're looking for, but I hope you'll find it interesting nonetheless.
A bit later than the conquistadores, but there were some Tierra del Fuegians who traveled with the HMS Beagle.
Orundellico, known in English as Jemmy Button (named because he was paid for with a mother-of-pearl button in 1828), traveled from Tierra del Fuego to London with three of his fellow Fuegians.
One died of smallpox, the other three came back and helped establish a mission at Woolya Cove in 1833. The English pastor nominally in charge of the mission, Richard Mathews, lasted a week and half before calling it quits and sailing away again.
Darwin wasn't really sure Button belonged back in the land of his birth - he was only a boy, and had learned English language and customs.
And there's a bit of an inkling in Darwin's descriptions of Button that the boy might have inspired some thinking about differences between people being cultural, not biological:
Jemmy Button was a universal favourite, but likewise passionate; the expression of his face at once showed his nice disposition. He was merry and often laughed, and was remarkably sympathetic with any one in pain: when the water was rough, I was often a little sea-sick, and he used to come to me and say in a plaintive voice, "Poor, poor fellow!" but the notion, after his aquatic life, of a man being sea-sick, was too ludicrous, and he was generally obliged to turn on one side to hide a smile or laugh, and then he would repeat his "Poor, poor fellow!" He was of a patriotic disposition; and he liked to praise his own tribe and country, in which he truly said there were "plenty of trees," and he abused all the other tribes: he stoutly declared that there was no Devil in his land. Jemmy was short, thick, and fat, but vain of his personal appearance; he used always to wear gloves, his hair was neatly cut, and he was distressed if his well-polished shoes were dirtied. He was fond of admiring himself in a looking glass; and a merry-faced little Indian boy from the Rio Negro, whom we had for some months on board, soon perceived this, and used to mock him: Jemmy, who was always rather jealous of the attention paid to this little boy, did not at all like this, and used to say, with rather a contemptuous twist of his head, "Too much skylark." It seems yet wonderful to me, when I think over all his many good qualities that he should have been of the same race, and doubtless partaken of the same character, with the miserable, degraded savages whom we first met here.
...
It was interesting to watch the conduct of the savages, when we landed, towards Jemmy Button: they immediately perceived the difference between him and ourselves, and held much conversation one with another on the subject. The old man addressed a long harangue to Jemmy, which it seems was to invite him to stay with them But Jemmy understood very little of their language, and was, moreover, thoroughly ashamed of his countrymen.
...
...Jemmy's mother and brothers arrived. Jemmy recognised the stentorian voice of one of his brothers at a prodigious distance. The meeting was less interesting than that between a horse, turned out into a field, when he joins an old companion. There was no demonstration of affection; they simply stared for a short time at each other; and the mother immediately went to look after her canoe. We heard, however, through York that the mother has been inconsolable for the loss of Jemmy and had searched everywhere for him, thinking that he might have been left after having been taken in the boat. The women took much notice of and were very kind to Fuegia. We had already perceived that Jemmy had almost forgotten his own language. I should think there was scarcely another human being with so small a stock of language, for his English was very imperfect. It was laughable, but almost pitiable, to hear him speak to his wild brother in English, and then ask him in Spanish ("no sabe?") whether he did not understand him.
...
I think we arrived just in time to save his life. Jemmy's relatives had been so vain and foolish, that they had showed to strangers their plunder, and their manner of obtaining it. It was quite melancholy leaving the three Fuegians with their savage countrymen; but it was a great comfort that they had no personal fears. York, being a powerful resolute man, was pretty sure to get on well, together with his wife Fuegia. Poor Jemmy looked rather disconsolate, and would then, I have little doubt, have been glad to have returned with us. His own brother had stolen many things from him; and as he remarked, "What fashion call that:" he abused his countrymen, "all bad men, no sabe (know) nothing" and, though I never heard him swear before, "damned fools." Our three Fuegians, though they had been only three years with civilized men, would, I am sure, have been glad to have retained their new habits; but this was obviously impossible. I fear it is more than doubtful, whether their visit will have been of any use to them.
...
Soon a canoe, with a little flag flying, was seen approaching, with one of the men in it washing the paint off his face. This man was poor Jemmy, -- now a thin, haggard savage, with long disordered hair, and naked, except a bit of blanket round his waist. We did not recognize him till he was close to us, for he was ashamed of himself, and turned his back to the ship. We had left him plump, fat, clean, and well-dressed; -- I never saw so complete and grievous a change. As soon, however, as he was clothed, and the first flurry was over, things wore a good appearance. He dined with Captain Fitz Roy, and ate his dinner as tidily as formerly. He told us that he had "too much" (meaning enough) to eat, that he was not cold, that his relations were very good people, and that he did not wish to go back to England: in the evening we found out the cause of this great change in Jemmy's feelings, in the arrival of his young and nice-looking wife.
...
Jemmy went to sleep on shore, and in the morning returned, and remained on board till the ship got under way, which frightened his wife, who continued crying violently till he got into his canoe. He returned loaded with valuable property. Every soul on board was heartily sorry to shake hands with him for the last time. I do not now doubt that he will be as happy as, perhaps happier than, if he had never left his own country. Every one must sincerely hope that Captain Fitz Roy's noble hope may be fulfilled, of being rewarded for the many generous sacrifices which he made for these Fuegians, by some shipwrecked sailor being protected by the descendants of Jemmy Button and his tribe! When Jemmy reached the shore, he lighted a signal fire, and the smoke curled up, bidding us a last and long farewell, as the ship stood on her course into the open sea.
(from The Voyage of the Beagle, 17 Dec 1832 to 5 Mar 1833)
Ships occasionally called on the area. The last record of Button is from the 1860s.