I totally agree with Macilrillein both major points: Alexander would have probably won but would not have been happy with his victory. and there is no reason why he would have gone west, as rome(or anything in italy) would neither pose a threat bigger than the persians nor provide with as much prestige and loot as the Persian empire.(IIRC)

if he had conquerd Rome (and some other tribes) before he went east(or instead) the rebellious and agressive romans would be his smallest problem, more annoying would be that continuing northwest would be totally pointless, Carthagian ships and most importantly the undefeated superpower in the east. maybe the persians would have conquered "ye known world" then. many people here are seemingly underestimateing the Persians and I'd like to add that Persia bashing is not a bit better than Rome bashing.

if we imagine he would have moved east after he'd conquerd the persian empire the roman rebels could have become sort of a problem but (aslong as he lives(or maybe one more reasonable successor than the historic Successors) ) the Hellenic empire would be powerful enough to just cut the gordian knot and do things that would have to be considered very brutal and wrong by everybody supporting a possible assasination of Alexander(or his Successor).

so Alexander would clearly have defeated the romans but it would be definately the wrong thing to do.

Ps: seems as if a new "It's you who are the barbarians!" discussion I would like to point out that Macilrillein is not a roman hater, and probably used it to give an account of Alexanders opinion on the romans rather than his own. afterall a Barbarian bascially is someone who does not speak the same language as yourself/is of different culture. I'm not exactly sure about Alexanders personal opinion as a macedonian who were often called barbarians by thier fellow greeks. But if Macedonias were considered Barbarians there is not the slightest doubt that the greeks of southern greece(and tarentum I assume) would reffer to romans(and samnites etc.) as barbarians.