The Empire, contrary to popular belief, was generally healthy. Its internal problems were (on the whole) no more severe than those of any other large empire in Antiquity. Alexander attacked at about the worst possible moment: after a bloody civil war / succession crisis had really fucked up the Empire, cost a lot of lives and money, and had eroded trust in the ruling dynasty among the local aristocracy (e.g. the satraps and their peers).
Without Alexander's invasion, the Empire can recover from the recent troubles. I reckon that it would, although poor administration can always screw things up. Even if that happens, the likeliest outcome is that another civil war occurs, and another dynasty basically takes over the Empire wholesale. The long-term effect of that is basically identical to the long-term effect of Akhaimenid consolidation: the shape of the Empire, its institutions and its culture are basically preserved.
In both cases, I think the loss of far-flung regions is almost certain. The Empire had used all its opportunities to expand, and the periphery was at this stage demanding more equal status. (That is: to be respected as part of the Empire proper, rather than as a barbarian fringe to be economically exploited). This means that the basic economic model of any and every imperial system (pumping revenue from the periphery to the core) had ceased to function. At that point, an Empire can hold on for two or three centuries yet (basically "living off the reserves")... but its ultimate death is already unavoidable.
I'd expect Egypt, (parts of) Anatolia and swathes of Central Asia (so, "old Parthia") to break off. The ATL equivalent to the Parthians will show up roughly on schedule to do what they did to the Seleukids in OTL.