I should note before I start that there's a series of blog posts currently being rolled out by Bret Devereaux that promises to address this exact question. The first post discusses the Spartan education and shows how it is just like the training of present-day child soldiers and terrorists. It is very explicit that these systems rely on indoctrination through trauma, and that inflicting trauma is an essential aim that ensures their effectiveness. It looks like the coming posts (dealing with the consequences of this upbringing) should be very interesting, and I recommend keeping an eye on the blog.

The problem with Devereaux' post is that he seems to be about 3 decades behind on the scholarship, and views on Spartan customs have changed a lot in that time. He doesn't seem to be aware of any of the major research done on the Spartan upbringing since Cartledge's work from the 1970s. Nigel Kennell and Stephen Hodkinson (among others) have done much to overturn the old idea that Spartan children were stolen from their parents at age 7 and raised to be killing machines. They focus instead on the values the education system meant to instill, and on the evidence that children (and adults) had a lot more going on in their life than preparing for war; they also point out that there's really no evidence that the upbringing involved any actual training for war. In their view, the Spartan education as it existed in the Classical period focused on creating good citizens, not good warriors. It was admired by other Greek elites because its cornerstones and chief goals were the same values they also pursued in the upbringing of their own children: obedience, deference to elders, and commitment to the community.

If this recent research is right, the Spartan upbringing would have been less traumatic than it is often presented, even if it was still marked by deliberate deprivation, subjection to physical and sexual abuse, and harsh punishments for transgressions. Children would have learned more than doing violence; they would still have seen their parents regularly; they would have had numerous things to look forward to in their "civilian" life, and not just face the endless drudgery of the army camp. The most violent and brutalising aspects of the system seem to date from a later period, since our only sources for them are Hellenistic or Roman, and Classical sources do not include them. So, to some extent, the idea that every Spartan child was meant to be scarred for life is questionable. Rather, many of the things boys also suffered elsewhere in the Greek world (such as beatings, the expectation to inflict violence on those of inferior status, and sexual abuse by adult men) were simply mandatory in Sparta.

In short, whether the Spartan upbringing caused universal and irreparable trauma is up for debate. But we can assume it here for the sake of argument. What effect did this have on the Spartiates, the male citizens who went through the education system?

Mostly, the answer is that we don't know. It's impossible to diagnose people from the past with this or that mental illness; we can't get a sense of someone's pathology without a personal interview. Worse, not a single Spartan from the Classical period has left us an account of their view of the world. The best we can do is look at how other people describe and judge Spartan behaviour. And it turns out it's pretty difficult to tell whether we're dealing with generally Spartan behaviour, or with the behaviour of a particular Spartan.

Take for instance the renegade Spartan commander Klearchos. He is described by the Athenian Xenophon, who marched with his mercenary army, as a figure who eats swords and breathes fire:

When he may enjoy peace without dishonour or harm, he chooses war; when he may live in idleness, he prefers toil, as long as it is the toil of war; when he may keep his money without risk, he chooses to spend it by waging war. As for Klearchos, just as one spends money on a boy or on any other pleasure, so he wanted to spend it on war. He was that much of a lover of war.

-- Xen. Anabasis 2.6.6-7

Some scholars interpret Klearchos as a man so affected by trauma that he became utterly brutalised, unable to stand peace or thrive in any civic environment. These traits are also seen in some modern veterans of war. But is this the result of his Spartan life and upbringing, or does it simply reflect an extreme personality, further warped by long service abroad? Xenophon knew many Spartans personally; he lived with them for decades, and sent his sons through the Spartan education. If this had been the normal way for Spartans to behave, why should he have described Klearchos' personality in such detail? Wouldn't he have appeared to Xenophon like just another ultra-violent Spartan?

There are many anecdotes in the sources about how Spartan commanders would discipline the men under their command by beating them with a stick, which other Greeks saw as excessive and undignified. But again, these are individual commanders acting violently against people they regarded as inferior, which wasn't unusual elsewhere in Greece; the physical abuse of enslaved people was completely taken for granted. The difference was that citizens (and even mercenaries) weren't used to being treated as social inferiors by their own allies, and weren't prepared to put up with it. As Simon Hornblower showed in his 'Sticks, stones and Spartans' (2000), the thing that galled the Greeks wasn't that Spartans were unsually violent or easy to anger, but that they treated free men like slaves.

Many other sources similarly describe the Spartans as ruthless and warlike. Thucydides has Perikles contrast the brutal discipline of Sparta with the freedom and leisure of Athens. Most readers of Sophokles' tragedy Aias read his enraged and pitiless Menelaos (king of Sparta), who insists that his men should fear him, as a commentary on the Spartans of his own day. But we can't read these texts as simple observations. Their authors are trying to make us think Sparta has gone too far, and that it's better to live in Athens. They are trying to stress the difference between Athens and Sparta at a time when the two states were at war. It doesn't seem likely that any wealthy Athenian could admire Sparta (as many did) if it was obvious to everyone that the Spartan system produced only furious brutes.

In short, the fact that our sources are so patchy, and that none of them are written by Spartans, makes it very hard to answer your question. On the one hand, the Spartans were certainly known to be terse, boorish, violent men whose only real skill was warfare. On the other hand, we don't even really know if this was a raw observation or a matter of biased stereotyping, let alone whether there was any connection between the Spartan upbringing and Spartan thought or action. Certainly the surviving voices from the period did not think the Spartan upbringing was a bad thing; rather, they idolised it, and subjected their own sons to it if they could. Many at Athens seem to have argued that it would benefit the city if a system like the Spartan one was introduced there as well.