How accurate would this be, seeing as he predates the rise of Christianity by at least 300 years? The exact quote from the song is "Hellenism he spread far and wide/The macedonian learned mind/Their culture was a western way of life/He paved the way for Christianity".
One could make such an argument, rather indirectly. Alexander's campaign took him to the far reaches of the known world, and this included Palestine. F. W. Walbank's The Hellenistic World says, "By the winter of 332 all Syria and Palestine was in his hands..."^1
One consideration to have in an answer to you is that in concentrating power in his person and de-emphasizing the traditional Macedonian/Greek elements of his rule in favor of a broadly "cosmopolitan, international" empire, he was creating the environment for his successors that had an independent character--Hellenism.^2 Hellenism would, through its spread, affect areas as close to mainland Greece as Italy and Anatolia and as far as Afghanistan, India, and Egypt. Nevertheless, the life of Alexander had nothing to do with Christianity. The lives of his successors or Diadochi, particularly the dynasty of the Seleucid Empire, did. The Seleucids (primarily) came to rule what we would consider the cradle of Christianity, and contemporaneously, Judaism. In ruling Judaea, the Seleucids controlled a territory from the immediate post-Alexandrian times to the onset of Roman control--which did not long precede the birth of Christ and the creation of Christianity.
Hellenism meant, in the long run, a syncretism of the Macedonian Greek culture of the foreigners and the local culture. There are other features of it that are less relevant to this discussion: realism in art and literature, an interest in sciences such as anatomy, geometry, philology, grander scale of architecture and the pursuit of more knowledge in general. The primary effect we will deal with is the religious development that necessarily occurred after the cultural convergence of very different peoples. "From the fifth century onwards the Olympian religion had been under attack. The sophistic movement had engendered a mood of scepticism about most accepted beliefs and at the same time many foreign cults had found a home in [Macedonian] cities..." Walbank explains that the milieu of these Hellenistic Greek led to "contact with non-Greek populations who worshipped different gods, the deliberate encouragement of certain cults for reasons of state policy." ^3 As odd as it may sound to our modern sensibilities, Judaism (and eventually Christianity) would be considered as just another cult religion.
The history of the Seleucids and the Jews in Palestine neatly interweave. The Jews were encountered nominally by Alexander, but became a well-defined faction during Seleucid rule in the third and second centuries. Walbank says of the Jews that they "possessed a religion, monotheistic and exclusive, which made it hard for the orthodox to come to terms with the Greeks around them or to acquiesce in the demands of Hellenistic kings." ^4 Because of this, and because of "the revolt of the Maccabees in the middle of the second century...of religious and nationalist motives [that] culminated in the violent Hasmonean rising..." the environment was created "in Palestine which made it fertile soil for the rise of Christianity two hundred years later." ^5 Indeed, it was in the context of the embattled and oppressed but Hellenized Jewry (which expected a chosen king to liberate them and return them to independence and righteous worship) that Christianity (with its promise of of salvation) sprang up. Paul was a Hellenized Jew, and he of course felt called to proselytize to Gentiles (Greeks/the population of the Hellenistic Greek world) as well as his fellow Jews. The early character of Christianity was consequently quite Greek. "Thus, in the form in which it was eventually to win acceptance as the official religion of the Roman Empire, Christianity was essentially the product of a mixed Jewish and Hellenistic environment." ^6 Therefore, in a roundabout way, his rule did indeed presage the appearance of Christianity, and Christianity has indeed been propagated and spread upon its initial program.
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http://www.fitzmuseum.cam.ac.uk/gallery/East-West/east-west_2.html