This is a pretty complicated question and, largely, is based on an interpretation of the histories of Alexander that is now considered unfeasible. That, however, doesn’t mean that there isn’t some truth to the claim. I don’t have the time to find my sources right now so this is going to be a bit informal.

Why it’s wrong:

Early modern Alexander scholarship was dominated by some British guy (sorry I don’t remember his name) who saw Alexander as basically a pre-Jesus. After Alexander finished with his conquests, he started taking on Persian customs and airs. The scholar saw this as proof of Alexander being an equalizing force: by elevating conquered Persians to the level of their Greek counterparts, Alexander was declaring equality of man. Christianity, which is a universal in its acceptance, spread easily because of the progressive framework wrought by Alexander’s liberal policies.

Enter Badian. Basically the old British dude was the premier Alexander scholar until Badian showed up, slapped him around, and took his throne. Alexander’s ‘persianization’ Badian said, was not an attempt at syncretism but rather an attempt to fully adopt the Persian system. Alexander’s position on top of the Greek world was rather tenuous: Athens and Sparta were constantly angling for independence and Alexander’s supremacy was only guaranteed through military might. In contrast, the Persian monarchal system was steeped in tradition and (largely) unwavering loyalty for their ruler. Furthermore, in terms of bureaucracy, the Persian system was significantly more advanced and efficient. Think feudal lords paying tribute (Greece) compared to a much more modern taxation and levy system (Persia). It was therefore in Alexander’s best interests to position himself as a successor to Darius III rather than as a foreign invader. Badian also did a lot of detailed textual analysis (both scholars based their conclusions largely on the works of Plutarch and Arrian) that made the British dude’s claims look silly.

Why it’s right:

Ok so this concept was created by the wishful thinking of some British historian who wanted to see Jesus everywhere he looked. It is not, however, completely without merit. Christian thought was not created from a vacuum but rather, in many ways, can be seen as an extension of earlier Greek thought: For instance, despite Augustine’s professed rejection of Greek thinkers, many of his arguments rest on distinctly Greek premises. The similarity can be seen quite easily: take a Greek concept like Plato’s allegory of the cave and replace the conclusion with Jesus/God’s love etc. and you get a rough approximation of Christianity. Aristotle can be such a boring read because (in the Judeo-Christian tradition) we have accepted his ideas so completely that they seem utterly dull and obvious. Furthermore, in many Christian traditions there’s some sort of intercession (usually by Mary) to rescue saintly sinners from hell. These sinners are people in hell who were not saved by virtue of being born before Jesus and are invariably composed of famous Greek thinkers.

Basically, the idea is that the universal acceptance of Hellenic ideals allowed for an acceptance of a theology that is created in a Greek framework. Furthermore, the lack of strict language/cultural/political boundaries allowed for dissemination of ideas across vast tracts of land. This created the perfect infrastructure for the spread of Christianity; which is already a pretty liberating and attractive ideology if you (as most non-elite people during this era were) are living in the shit.

Maybe only very indirectly...you could argue that it was the state that he created enabled Aristole (contemporary of Alexander, circa 322BC) and the other famous Greek philosphers to flourish so that when the Romans arrived they adopted and perpetuated a lot of the work (and the Greek language) and spread it far and wide to...Judea. Early Christianity was fairly popular and (also) persectued until the early 4th Century.

Greek philosphy has always been very popular though and its schools of thought have a large influence even today. If you run with that thread, I guess you could say that if it wasn't for the stable and rich state that Alexander the Great and his father Philip were able to secure, we may have lost some of the great Greek thinkers.