Would the events of the invasion unfold the same way, though? Artaxerxes' failure maight lead to a different succession for Darius III, or a different outcome for the last years of Philip's reigns, up to him surviving (no assassination attempt, or it fails, or it hapens and succeeds at a different date) all of tht could affect the Macedon-Persia dynamic a lot.
However, there's potential for clash between Egypt and Macedon even before they're finished with the Persians, as they would likely compete for dominance in the Levant. In that case, the Persians might consider retrenching East of the Euphrates and bide for time.
If such a situation stabilizes (a that's a big if) it would be (very roughly) convergent with OTL's Hellenistic Age in geopolitical terms, with three major powers based in Asia (though further East than OTL Seleucids) Egypt and Macedon. That seems to suggest that the basic trend of the era was conducive to something of the sort. Of course, culturally it would be very different.
That's the best analysis of what might happen after the POD.
But there was one possibility though which Falecius did not mention:
Macedon might decide to invade ATL Egypt instead of the Persian Empire. Independent Egypt might be a hard nut to crack and with a longer period of independence even after the conquest the prolonged period of the Egyptian resistance to the foreign domination might follow.
So the Macedonians would not be able to immediately after taking Egypt start a war against the Persian Empire. And in this ATL the Persians would have more time to get prepared against the Macedonian aggression. And if Macedon started an invasion to Persia after Egypt that Egypt in the Macedonian rear would be different from OTL - that would be Egypt proud of his former victories against World Persian Empire and with memory of their own Egyptian Empire - so Macedon would be painfully aware of a possibility of revolt in Egypt anytime or with actual revolts.
And there was another consequence of independent Egypt:
The Persian Empire might get disintegrated to some extent as the Persians lost a war against Egypt and showed signs of weakness to their restive subjects.
Let's say all the lands to the West of Mesopotamia were lost to Persia - and that would be VERY different world.
And I would not be too sure that taking a bunch of independent countries instead of one unified Empire would make it any easier for Macedon. At least holding these lands and consolidating would take much more time than in OTL. In OTL Alexander said to his conquered subjects - now I am King of the Kings instead the former one you had and the rest is the same - what you paid to him you would pay to me.
In this ATL Macedon would have to conquer all these countries anew and get them acquainted with foreign domination once again.