One of the things about the really large Persian Empires is that they weren't really strongly controlled by the center anyway. The Empire maintained a strong army that could deal with invaders or the odd independent minded governor, but on the whole most of the Empire was rather self-governing. With a 14 year old to succeed Alexander, then you could easily see much of Alexander's Empire split up as it was OTL, only under the auspicies of Alex's Heir's Empire. The boy would have the general's loyalty probably by dint of his lineage, and the Imperial ruling class is going to be pretty exclusively Greek ruling over a bunch of different groups, so this shared culture could provide the glue to hold the Empire together, a ruling culture based in the cities that Alexander has founded across his conquests. With an Empire this large, then I think that once trade restarts you're going to have a lot of tax revenue and thus wealthy governors, whose wealth is tied to the continuance of the Empire. Thus you have wealthy governors, who are happy governors, with a stake in a continued empire.
Alex's Heir is probably going to be married to a Persian princess in this TL, rather than Alexander himself, or maybe in addition to. The Imperial army, with its reliance on Macedonian infantry, could be an agent of hellenization, as OTL the Roman Legions were of romanization. Now eventually you're going to have barbarian invasions, regional powers nibbling at the edge of the Empire, and corruption at the center, all contributing to the collapse. However, in the meantime you're going to get a rather intense period of hellenization and a massive arena for the flow of ideas from East to West and vis versa that will have major knock-on effects in the Empire, and in the periphery of the Med, Central Asia, and India.