The story is in fact featured in 3 of the 5 surviving accounts of the life of Alexander the Great. The most detailed account is in Curtius Rufus, but we get a neat potted version in the universal history of Diodoros of Sicily (1st century BC):

When Alexander returned to Hyrkania, there came to him the queen of the Amazons name Thallestris, who ruled all the country between the rivers Phasis and Thermodon. She was remarkable for beauty and for bodily strength, and was admired by her countrywomen for bravery. She had left the bulk of her army on the frontier of Hyrkania and had arrived with an escort of three hundred Amazons in full armour. The king marveled at the unexpected arrival and the dignity of the women. When he asked Thallestris why she had come, she replied that it was for the purpose of getting a child. He had shown himself the greatest of all men in his achievements, and she was superior to all women in strength and courage, so that presumably the offspring of such outstanding parents would surpass all other mortals in excellence. At this the king was delighted and granted her request and consorted with her for thirteen days, afterwards he honoured her with fine gifts and sent her home.

-- Diodoros 17.77.1-3

All versions of the story are basically the same, and clearly derive from the same source. Plutarch lists several other authors who also included it in their works, though none of these survive:

Here the queen of the Amazons came to see him, as most writers say, among whom are Kleitarchos, Polykleitos, Onesikritos, Antigenes, and Ister.

-- Plutarch, Life of Alexander 46.1

So far so good, bro. It should be said that all accounts agree that only the Amazon queen herself was looking to get pregnant by Alexander - not the 300 women of her bodyguard. Still, it seems that a broad range of ancient authors believed that Alexander spent 13 days making sweet love to Thalestris, who wouldn't leave until she "thought herself pregnant" (Justin 12.3.7).

But here's where it gets interesting. Plutarch continues:

...but Aristoboulos, Chares the royal usher, Ptolemy, Antikleides, Philo the Theban, and Philip of Theangela, besides Hekataios of Eretria, Philip the Chalkidian, and Douris of Samos, say that this is a fiction.

Note that this list includes Ptolemy, one of Alexander's most trusted generals, who would have been there to see it for himself. Plutarch also tells the story that when someone read this part of Alexander's biography to Lysimachos - another one of his closest men - Lysimachos replied sarcastically, "and where was I at the time?" In other words, he knew of no such event, even though he was there with Alexander when it supposedly happened.

Finally, Plutarch cites no lesser authority than Alexander himself to refute the story. He claims (Life of Alexander 46.2) that Alexander wrote a letter describing events in remote Hyrkania to Antipater, who was the steward of Macedon and Greece in his absence. Alexander wrote only that a Skythian king offered his daughter's hand in marriage, and nothing else.

On these grounds, the whole story starts to look rather unlikely even if we believe - as Plutarch probably did - that there were tribes of Amazons living in the remote steppes of Skythia. Our own understanding of the way the Greeks looked at Skythia allows us to be even more skeptical. While the women of the nomadic peoples of the region may well have fought alongside the men, the Amazon is a creature of Greek myth, a barbarian Other, the deliberate opposite of everything that Greek civilisation stands for. Quintus Curtius in particular makes it very clear that the Amazons of his story are the impossibly alien mix of Skythian stereotype and ethnographic fantasy that the word "Amazon" conjured up in the Greek mind since at least the 5th century BC. In his story, they are a tribe composed entirely of women, who mutilate their right breast in order to better use the bow and javelin, and who dress with the left breast exposed in order to nurture their daughters. Thalestris says she will only keep the child if it is female; if she gives birth to a son, she promises, she will return it to Alexander. The list goes on. This description of a supposed tribe of warrior women seems largely cribbed from Herodotos and others; since Alexander would not have encountered any such tribe on the actual steppe, the account had to be fleshed out with "common knowledge".

The story of Thalestris, then, was not derived from the historical accounts compiled by Alexander's companions or their later successors. Instead, it was a feature of the so-called "Alexander Romance", a mythologised tale that sprung up not long after Alexander's death and is the ultimate source for many of the most outrageous, superhuman and incredible aspects of Alexander's story. Because it is so much more focused on Alexander as a larger-than-life character, affecting everything he came into contact with, the Romance has proved fertile ground for people to develop their own stories and myths. But it is not generally taken seriously as a historical source.

Since none of the surviving accounts of Alexander's life are contemporary sources - we don't have the work of Ptolemy, for instance, only that of people who read Ptolemy - it can be difficult for us to sift fact from fiction. In all sources we have, history and Romance are blended in ways we can't always discern. But in this case, at least, Plutarch preserves for us a glimpse of the debate that raged in his own time about which parts of Alexander's story to accept. And he ends his discussion with these soothing words:

However, our belief or disbelief of this story will neither increase nor diminish our admiration for Alexander.

The story you're referring to shows up in Curtius:

There was, as was said before, neighboring on Hyrcania, a race of Amazons, inhabiting the plains of Themiscyra, about the river Thermodon. They had a queen, Thalestris, who ruled all who dwelt between the Caucasus mountains and the river Phasis. She, fired with a desire to visit the king, came forth from the boundaries of her kingdom … she came forward attended by three hundred women, and as soon as the king was in sight, she herself leaped down from her horse, carrying two lances in her right hand.

[Curtius then digresses for a moment on the dress and customs of the Amazons, also the fact that barbarians like showy things.]

However, on being asked whether she wished to make any request, she did not hesitate to confess that she had come to share children with the king, being worthy that he should beget from her heirs to his kingdom; that she would retain any female offspring but would return a male to his father.

Alexander doesn't send the lady home wanting, instead he spends thirteen days "satisfying her desires."

While the story is fun, it's definitely not true. For one thing the Amazons are a fictional race and, though there may be germs of reality in their construction, there is certainly nothing like an Amazonian nation at this time.

To put it in the words of Arrian, one of Alexander's early and relatively sober biographers:

They say that Atropates, the viceroy of Media, gave him a hundred women, saying that they were of the race of Amazons. These had been equipped with the arms of male horsemen, except that they carried axes instead of spears and targets instead of shields. They also say that they had the right breast smaller than the left, and that they exposed it in battle. Alexander dismissed them from the army, that no attempt to violate them might be made by the Macedonians or barbarians; and he ordered them to carry word to their queen that he was coming to her in order to procreate children by her. But this story has been recorded neither by Aristobulus nor Ptolemy, nor any other writer who is a trustworthy authority on such matters. I do not even think that the race of Amazons was surviving at that time; for before Alexander's time they were not mentioned even by Xenophon, who mentions the Phasians, Colchians, and all the other barbaric races which the Greeks came upon, when they started from Trapezus or before they marched down to Trapezus. They would certainly have fallen in with the Amazons if they were still in existence.

[Arrian debates for a while over the evidence that Amazons ever existed, before concluding:]

If therefore Atropates showed any equestrian women to Alexander, I think he must have shown him some other foreign women trained in horsemanship, and equipped with the arms which were said to be those of the Amazons.

There is a really interesting question though of WHY the Alexander biographies involve such a bizarre and patently false story. There have been some interesting suggestions. Obviously the Amazons create an element of erotic and exotic fantasy (in your words, cool story bro), but there seems to be a bit more to it. For one, either Alexander himself or his biographers was trying to associate him with Achilles (with the emphasis on his brooding alone in his tent and his close friendship with male companions). Achilles also fights, kills, and falls in love with - in that order - the Amazonian queen Penthesilea. In Curtius' account, there seems to be something a little different going on. Curtius is interested in the contrast between Alexander's Greek rationality and barbarian passion. Submitting to the desires of the Amazonian queen is one of the precipitating events in Alexander's surrender to barbarian passions.

If you're interested in learning more Elizabeth Baynham was written/edited a number of articles and books on the topic.