The odds would be pretty good (well, except for the Arabian Peninsula, as Alexander did not campaign there). Whilst the army did not stay singular throughout the entire campaign - people were left in various locals to rule, protect supply lines, et cetera - the core of his army that he entered India with was made up of the same troops he began the war against Persia with. So, if you were a soldier under Alexander's command and survived the various battles, campaigns, and marches, you could have fought under him from Anatolia all the way to India.

The fact that his troops had been away from home for such a long period of time was certainly one of the causes of their mutiny in India, which put an end to Alexander's journey east.