I know of the Sacred Band of Thebes and I'm curious how it was in other armies, if it was institutionalized at all.
To start, historians like Percy III, claim pederasty came to Greece with the Dorians, an ethnic group which the Spartans were part of. It originated in Crete around 630 BCE with older men kidnapping young boys, and from there spread to Sparta (Source: Reconsiderations about Greek Homosexualities")
Speaking of Spartan upbringing and military practice, Plutarch writes in Life of Lycurgus:
When the boys reached this age, they were favoured with the society of lovers from among the reputable young men. The elderly men also kept close watch of them, coming more frequently to their places of exercises, and observing their contests of strength and wit, not cursorily, but with the idea that they were all in a sense the fathers and tutors and governors of all the boys.
Something also to note about the Spartan's is their rituals involving the consummation of marriage according to Plutarch:
For their marriages the women were carried off by force, not when they were small and unfit for wedlock, but when they were in full bloom and wholly ripe. After the woman was thus carried off, the bride's-maid, so called, took her in charge, cut her hair off close to the head, put a man's cloak and sandals on her, and laid her down on a pallet, on the floor, alone, in the dark. Then the bride-groom, not flown with wine nor enfeebled by excesses, but composed and sober, after supping at his public mess-table as usual, slipped stealthily into the room where the bride lay, loosed her virgin's zone, and bore her in his arms to the marriage-bound. Then, after spending a short time with his bride, he went away composedly to his usual quarters, there to sleep with the other young men.
Expanding more on Sparta; since there was a fracture of the family unit by way of intervention of the state, pederasty may have served a very important part in the upbringing of young Spartiates. A suitor would have educated the boy in athletics, military tactics, and "manliness." There's a legend about Sparta where after a boy cried out in pain during a fist fight the boy's lover was punished for not teaching him manliness.
Victor Davis Hanson claims these strong bonds would have helped unit cohesion and order in battle; it developed a sense of trust and enhanced morale. The separation of sexes from an early age, he states, would have lead to homosexual liaisons in the male barracks ("Western Way of War").
Plutarch also mention's an off hand remark by Alexander the Great's father, Philip II -
"It is not only the most warlike peoples, the Boeotians, Spartans, and Cretans, who are the most susceptible to this kind of love but also the greatest heroes of old: Meleager, Achilles, Aristomenes, Cimon, and Epaminondas."
Philip II may have been inferring that societies which held the "Homeric" ideals produced the best warriors. In the Iliad Achilles and Patroclus are assumed to be lovers, though homosexuality is never openly stated. However, the Iliad was most likely not written during the actual time of the Trojan War, so it's possible that "homosexuality" in the earlier period around Troy (11 or 1200's BCE) was more of a platonic admiration or affection. This would then mean that Homer's society added layers of sexual desire that better reflected their ideals.
According to Diodorus Siculus, Epaminondas, Thebes' greatest general, had two lovers who came on campaign, fought and even died next to him.
Also, in Thebes, a suitor may have provided a panoply (set of armor) for his younger lover.
Military pederastry may have risen with the citizen hoplite in the 600's BCE (if one holds the view that hoplites even existed back at this point) as part of a set of sweeping military reforms happening throughout ancient Greece. The Greeks tended to associate homosexuality with manliness. Also noted is the Ionian Greeks of Asia Minor, who were considered militarily inept and "soft", were the least interested in homosexual affairs ("Dictionary of Ancient Greece").
It's hard to tag what exactly "homosexuality" was in practice for the Greeks. For the most part the Greeks advocated control of one's sexual desires and any sexual conduct may have been highly ritualistic. On top of all that, customs varied region to region. Sex, however, in writings and depictions has the undertones of power and authority, rather than perverse sexual desires.
Xenophon, contrary to other authors, actually insists that Spartan law punished any man who had sexual conduct with a boy. Plato also speaks of this bond as a more platonic love that is about personal growth and proper upbringing.
Summary: There's evidence for it, especially in militaristic societies, however, it's still hotly debated and even the contemporary authors provide contradictory views on the subject.
Note: I'm not an academic, but I have an interest in Greece/Macedon
Edit: Searched my library and found more info: The Sacred Band of Thebes, according to J.E Lendon, was the epitome of the competitive hoplite spirit. The reported advantages of this unit was the competition between the warriors; lovers competed to be the best and were less likely to run or do something shameful in front of each other. At Sparta couples stood together in the battle line and the Spartan's sacrificed to Eros (love).
The Theban general Pamamenes, alluding to the homoerotic bonds of the Sacred Band, jokingly said Nestor (general from the Iliad) "was no tactician when he ordered the Greeks to dispose themselves in units by brotherhoods and tribes, and let each brotherhood go in support of brother hood, let tribe support tribe, because he ought instead to have stationed lover by beloved." This also gives credence to the theory that Homeric male eroticism was not sexual and that Classical Greeks added those overtones.
The question of pederasty in Spartan Society is a hotly debated topic. The Spartan Myth approach is stated in the first response. It is important to note that most of the ancient commentators had no first-hand experience of Sparta, were from its rivals and therefore had a vested interest in besmirching Sparta, assumed that Sparta was just like their own society and that this behaviour was normal, and/or, were from a completely different era.
A New Perspectives of Ancient Sparta school of historians has emerged that challenges the oft quoted 'norms' as they are accepted, and put forward new ideas. Stephen Hodkinson and others lead this changing viewpoint. Here are some of these results on this topic.
Helena P. Schrader; “No myth about Sparta is as persistent and controversial as the insistence that pederasty and homosexuality dominated Spartan society. Even highly reputable historians such as Paul Cartledge subscribe to this theory. However, the evidence against it is compelling.”
Xenophon, the only historian with first-hand experience of the agoge (his sons attended it!), states explicitly: "… [Lycurgus] … laid down that in Sparta lovers should refrain from molesting boys, just as much as parents avoid having intercourse with their children or brothers with their sisters."
Xenophon adds: "It does not surprise me, however, that some people do not believe this, since in many cities the laws do not oppose lusting after boys." This is the crux of the matter. All of our written sources on Sparta come from these other cities, where pederasty was rampant.
Aristotle, blamed all of Sparta's ills on the fact that the women were in control of things – a fact that he attributed to the lack of homosexuality in Spartan society generally.
Herodotus, who was always happy to provide some juicy little story has not a single tale in which there is mention of a Spartan with a male lover – either boy or man. This omission is significant and should not be ignored.
While pederasty is as frequently depicted in Athenian and Corinthian art as heterosexual sex, no homoerotic art originating in Sparta has to date been found or identified.