On grounds of "Give-a-guy-chance" sentiment, I feel somebody should run with this. Let's take the POD itself:
Rather than assume 30 years, let's just assume Alexander survives at Babylon. The first question is does he keep conquering or does he spend time consolidating his holdings? Most people figure the former, but I've always thought that he'd need to do something to husband everything he's just acquired. Given the revolts in Greece which sprang up after his death in OTL, Alexander's empire is far from secure, even barring the wars of the Diadochii. He might spend some time founding colonies, building roads and cities. In short he tries to drain as much of mainland Greece's population as possible into the former Persian Empire: this will lessen the abilty of the members of the League of Corinth to resist his rule and increase the unity and strength of his new Graeco-Persian realm. This time gives Alexander the ability to train a new army according to new tactics he's learned in his conquests. A few of his generals also take their places as governors of provinces, but none will question Alexander's rule.
As far as the direction of conquest, I think given time Alexander will chose to go Westwards. He knows there are more lands in both directions, but at some point Carthaginian activities in Sicily may offer the opportunity for a new Pan-Hellenic Crusade of Conquest. This war will be far different than the first, since Alexander will have to make use of ships. However, the Greeks of Athens and Corinth will probably like this because they will be enriched as they row in the conquerer's fleet. Alexander thus conquers Sicily and Italy and adds the Greek states there to the League of Corinth. If successful, he presses the advantage and swallows the entire empire of Carthage and continues on to Spain. Again, I think Alexander's impetus in a Westward campaign is to consolidate his holdings vis-a-vis the effects on Greece of such an expedition.
The other major hurdle is the question of succession. Even if Alexander has an heir, how compotent will that heir be at ruling such a far-flung empire? How loyal would the great variety of generals and local rulers remain to a new King? What kind of governance would grow out of the monarchy and the League of Corinth to effectually govern the pan-hellenic domains. In my opinion, unless Alexander has also managed to spend a substantial amount of time building up a bureacracy, the empire will quickly crumble after his death, even with an heir. The heir will not have Alexander's character nor his exploits. Unless he conquers another contintent, which at some point will be very difficult, the empire will splinter.
The hard part of assessing the effects is that they will be either cultural or demographic, and hence prone to all sorts of chaotic variations (the butterfly theory). At the very least, the proposed outline is possible--except perhaps for the necessity of Christianity; far more likely something like Zoroastrianism emerges to unite Greek and Persian nobles.