Unless you're trying to tell me that Alexander turned the people all the way to the Indus into greek culture adherents, no, Alexander's empire wasn't a society.
It's important to note here that Alexander created a short-lived empire - he did not create the society we think of as 'ancient greek'. That pre-existed him quite considerably in greece. And just because he gathered Perseopolis into his fold doesn't make the society there 'greek'.
The original poster posited that Ghengis Khan's activities birthed the society. Alexander's activities did nothing like this - the society was already there, and greek culture was fairly widespread to begin with, though perhaps not in the direction of the Indus. When Alexander died, the Greeks didn't fade away to become background players again - they were a powerful political and especially social force for centuries to come... largely in the opposite direction to Alexander's conquests.
Alexander was an incredible conquerer, but he did not make nor break Greek civilised society.
