There definitely was interchange between various Greeks and Buddhists since Mahayana Buddhism's early development was in much contact with the Greeks from Hellenistic kingdoms in Bactria and India and some of those Greeks converted to Buddhism:
https://en.wikipedia.org/wiki/Greco-Buddhist_monasticism
Gandharan Buddhist art is steeped in Greek stylization and the first images of the Buddha followed Greek stylizations - early Buddhists didn't depict the Buddha at all, just symbols like empty footprints, it wasn't until Greek contact that this began.
Thomas McEvilley's _The Shape of Ancient Thought: Comparative Studies in Greek and Indian Philosophies_ has an interesting discussion of similarities between earlier Stoic texts by Sextus Empiricus and some works of Nagarjuna (one of the most important Mayahana philosophers) that use the same arguments, metaphors, and structuring. He goes over a number of other ancient sources, Greek and Indian, describing various sorts of cultural contact and interchange.
Pre-Hellenistic contact between the Greeks and India occurred but we can only speculate about it since there's no reliable evidence. After Alexander there was a lot of interchange and it had a big impact on Indian art, architecture, theater, and culture (as well as bringing significant influence of Indian stylization, philosophy, etc. on Greek Hellenistic kingdoms in Bactria and India).