There are all kinds of speculations as to how he could conquer China, unite Eurasioa under some kind of enlightened rule, and bring peace to the earth (Toynbee, IIRC) or how he would attack Rome and be beaten (Livy), but personally I'll buy none of it.
Given he inherited his father's constitution (doubtful - Philip had a health like a horse while Alexander sounds more like burning the candle at both ends, using up energies he would have needed in his 40s), he might have survived his bout with whatever killed him like he survived a lung puncture and all manner of other nasty wounds. To be in the realistic timeframem give him another 20 years (most men who lived to be 30 could hope to live to be 50 or so - it was infancy, youth, and, for women, the childbearing years that were dangerous). If he had suddenly seen the light and become a radically different person (it happens - just look at any number of Born-Again religious folk) he could have done some good, even. But look at the man for a second:
- he turned down an honorable and incredibly lucrative, not to mention sustainable peace in favor of world conquest
- he killed his best friend in a drunken rage
- he burned down one of the richest, most beautiful cities in the world ditto
- he was so angered by successful resistance he crucified every male inhabitant of Tyre
- he was given to publicly humiliating his best generals ("If I were Parmenion, so would I" - yeah, great way of making friends, Al)
- he killed thousands of his own troops, very likely by design (though if you accept that it was sheer stupidity that doesn't exactly make him look good)
- he fought in the thick of battle while he was needed in operational control
- he demanded to be treated as a God towards the end of his life - likely without ever understanding what god-kingship in the Orient meant and did not mean
- he quite probably had his own father killed
To me, that reads 'egomaniac'. Possibly even more. He's certainly not someone I would want in government, having delusions of omnipotence like that (note: it might be a good idea to vote for the candiate who promises least as the chances are greatest he actually thought about the feasibility of his plans). Would he have presided over an age of peace? I don't think he had any intention of doing sop. Peace bored him, and there was a world to conquer out there. His interest in the Persians as recruitment material was very likely motivated by the need for more pliable soldiers, and lots of them (his Macedonians and Greeks had just learnt the price of standing up to Alexander). India might have been next on his target list, but I suspect Carthage. Unless the Carthaginians gave up quickly (unlikely), they would have been in for a treatment that matched that at the hands of Rome. It had worked for Thebes and Tyre, after all... That would put him in a position to dominate the Western Med, at which point he would probably collect the submissions of numerous tribal chiefs and lose interest. like he did in Central Asia. Perhaps he'd see potential in Italic, Celtic or Numidian soldiers for his next big campaign. You can bet there'd be one.
What I'd predict is that a longer life for Alexander simply means a bigger empire to eventually collapse, and perhaps less of a heroic stature as the disintegration would probably begin in his lifetime. A more widespread Hellenistic civilisation is also likely, at least in the Western Med, which might nix Rome, but would almost certainly destroy any prospect of Latin becoming a second western language (Pontus, Bithynia, Cilicia, Parthia and Bactria became significant non-Greek powers, but their riuling classes all spoke Greek and lived in a Greek world. I could see a similarly Graecised Latin League or Samnium becoming the dominant power in the Western Med). Driving all the way to India or China might similarly extend Greek culture, though I don't think it would be as easy. In fact, facing the Chinese armies of the Warring States period might just give him the lesson in humility he should have gotten in 333. A (more likely) conquest of India might open the path for Buddhism to the West (the Greeks did not much care for foreign writings, but the Sutras might have been translated just as the Septuagint was, and the missionary impulse was certainly there). That opens up all kinds of possibilities.
Still, on the whole I don't see any of the prospects as desireable. Even the bit about 'Spreading civilisation' and 'creating an integrated cultural sphere' tends to be much overrated. We need to balance what we gained (A Greek cultural sphere throughout the East) against what we irrevocably lost (all the literatures and literate civilisations the Greeks did not care to learn about and consequently never translated, collected or read the writings of). The role of Greek as a cultural medium of communication tends to be overrated (the East did quite well with Aramaic) and frankly, I prefer what little Carthaginian, Syrian or Persian art survives to the rather anodyne glories of Hellenism. But that's a matter of taste.
