How widely read was "Anabasis" at the time?
The Greek sophist Eunapius (about 4th century AD) wrote this in his 'Lives of the Sophists', a collection of biographies of philosophers:
'Xenophon the philosopher, who is unique among all philosophers in that he adorned philosophy not only with words but with deeds as well (for on the one hand he writes of the moral virtues both in discourses and historical commentaries, while he excelled also in actual achievement; nay more, by means of the examples that he gave he begat leaders of armies; for instance great Alexander never would have become great had Xenophon never been)' -Lives of the Sophists
So this suggests Xenophon influenced Alexander in his ambitions as a conqueror.
This article, I'm not sure about its credibility, investigates the question 'Did Alexander the Great read Xenophon?', so I suggest you read that.
I don't think there's any hard evidence to support this though.