Taking over all of Persia and Hellenising it? I sense that's pretty ASB. The Achaemenids treated their non-Persian subjects pretty well and adopted some sort of federal system so Alexander's chances at gaining the loyalty of the many locals necessary to build an army the size of the Persian army fall to a point where not even that famous Italian general accompanied by other two or three of his kind could achieve victory. At maximum, I can see Alexander marching down through the Bosphorus and liberating the Greek Ionian cities and maybe stablishing control over Galatia and other territories in Asia Minor but I honestly can't see that Greek boy going further than the Taurus mountains. Also, it seems that his personality was pretty impulsive and unpredictable, maybe he takes some crazy decission that drives his whole campaign to disaster, possibly killing his own generals or taking a wrong path which leads the Persians to his rearguard.