Not so far as we know! There are five surviving tertiary sources for Alexander, several hundred years removed from the events. Thanks to Arrian's in-depth military account in Anabasis Alexandri, we have a pretty clear idea of Alexander's location between 334BC (crossing the Hellespont) and 323BC (death in Babylon). Considering his desire for conquest and the long overland travel time of that era, it's unlikely he would have had time for return trips to Greece. Ancient warfare often involved extremely long campaigns. Antipater served as regent of Macedon and Greece during Alexander's campaigns until the latter's death in 323BC.
Here is a map of Alexander's route
During his Persian campaign, Alexander's ability to return home by sea (had he wanted to) was hampered by the naval superiority of the Persians. Thereafter, Alexander travelled further inland, making return trips to Greece infeasible. As the years dragged on, Alexander's army became ever more ponderous, as his forces grew and his men were weighed down by loot (or as Plutarch eloquently states, charged with booty). At the outset of his Indian campaign, Alexander actually burnt many of his baggage wagons to unburden his army.
We know that Alexander's army bid him to return to Greece when he marched east into Mesopotamia. Plutarch notes in Life of Alexander:
Certain it is, that apprehending the Macedonians would be weary of pursuing the war ... [Alexander] spoke to them to this effect: ... if they should think of returning when they had only alarmed Asia, and not conquered it, their enemies would set upon them as upon so many women. However, he told them he would keep none of them with him against their will ... that when on his way to make the Macedonians the masters of the world, he was left alone with a few friends and volunteers. This is almost word for word, as he wrote in a letter to Antipater, where he adds, that when he had thus spoken to them, they all cried out, they would go along with him whithersoever it was his pleasure to lead them...
By the time Alexander reached the Indian subcontinent in 326BC, his army had been campaigning for nine years. It took the near mutiny of his men - homesick and faced with a united India - to turn Alexander back. Plutarch writes regarding the aftermath of the Battle of Hydaspes:
But this last combat with Porus took off the edge of the Macedonians' courage, and stayed their further progress into India.
The refusal of his men to continue into India apparently caused Alexander great grief, and it was difficult to convince him to abandon the campaign. He first tried the same tactic he had employed in Mesopotamia, but to ill effect. Arrian:
But the next day he called the same men together again in wrath, and told them that he intended to advance farther, but would not force any Macedonian to accompany him against his will ...
But on the contrary, when there was a profound silence throughout the camp, and the soldiers were evidently annoyed at his wrath, without being at all changed by it ...
It would take him 2 years to return to Persia, arriving in Susa in 324BC and thereafter traveling to Babylon in 323BC.
It's worth noting that Alexander did send men home after battles, often with rewards of land and wealth. Although he received some reinforcements from across the Hellespont (See /u/Fogge's answer here) his army became increasingly Persian and Asian over the years. Eventually the Persianization of the army, and Alexander's own adoption of Persian customs led his Greek soldiers to threaten revolt in 324BC.
Sources
Edit: wording
