if after 500 years, another ship arrives from Byzantium, would the Byzantines be able to understand the language of the colonists, or would the two varieties of Greek have diverged so much by this point that the groups would not be able to understand each other?
OK, I'm not a linguist. So, I can't say how or how much would language change in 500 years after being isolated. I suspect there are people a lot better equipped to answer that. To me, it seems that 500 years is not insignificant - it's between 20-25 generations (a generation is about 20-25 years "long"). It's also not "excessive" - we can trace back some words and phrases today for about that long. Sure, texts from 500 years ago might seem archaic at best or barely intelligible in other cases but we have some that we can understand without needing to be trained specifically.
However, what I do know is Byzantines. OK, I'm not an expert or anything but I have a passing fascination with the Eastern Roman Empire. So, I feel more confident I can (at least partially) answer the question from that side.
Were "old" and "new" Byzantines to meet, they'd be able to understand each other.
Not without some initial difficulty but it wouldn't be THAT hard.
Some background clarification first: the Byzantine empire was never called "the Byzantine empire" during its existence. It was the Roman empire. People living there were Roman and would call themselves Roman. After the East/West split of the empire and the collapse of the western part, the eastern just...continued existing. Nothing radically changed for them. However, the Eastern Roman Empire was also Greek. People spoke Greek and used their Greek customs. They also knew Latin, for when needing to speak to people from the Western part but the Greek cultural identity was rather strong.
Speaking of people in higher positions, they'd also read and study old Greek writings. Of philosophers, playwrights, writers - cultural heritage is something they not quite revered but valued greatly.
So, the old was preserved. People in the new world would most likely keep some reference of the "old language" - even with a language drift, there would still be people who would read and understand the old texts. The elite would very likely be educated in old Greek, too, even if out of tradition.
Aside from protecting the old heritage, the Hellenistic culture was rather aggressive in protecting itself from outside influences. Not to zealous levels but the Eastern Romans generally disliked using foreign words and terms, if they could help it. They'd translate or at least Hellenise a word. If possible, they'd use an existing one instead of a foreign term, even if it doesn't match correctly. In fact, the title Imperator was translated as "Autokrator" (self-ruler) in Greek. Many other titles had a Greek equivalent to keep outside influences - "doux" for "duke", "comes" (kom-es) for "count". Even the very official Latin title of an emperor Augustus was sometimes translated as "sebastos" in Greek. Not for very long at least in terms of referring to the emperor as sebastos - the Greek title continued existing for other officials.
Somewhat fun fact with some side-tracking: eventually the emperor Heraclius changed his full title from Imperator Caesar Flavius Heraclius Augustus (which could be even "fuller" as Emperor Ceaser Flavius Heraclius, faithful in Christ, most serene, supreme, beneficient, peaceful, victor over the Alamanni, the Goths, the Franks, Germans, Antae, Alans, Vandals, Africans, Heruls, Gepids, pious, fortunate, glorious, victor, triumphant, ever venerable Augustus) to the Greek "Basileus" (pronounced vas-ee-levs) which literally meant "king". However, Roman Republic did not have kings - the title in common usage referred broadly "ruler" and then came to mean "the ruler of the Roman Empire", so equivalent to "emperor". This was only used for the emperor of the Roman Empire - foreign rulers would usually be referred to as "rex", a Hellenised term for "king" that applied to other (barbarian) rulers.
Side-track over, this was (in part) another way for the Hellenic culture to reject "outside" influence and preserve its independence.
All that is to say that the Byzantines are highly likely not only to preserve at least some of their old ways but will also reject overt "barbaric" influences.
Since the original Byzantines would also act in a similar fashion, when the two re-join, they should be able to communicate. They should have enough commonalities to overcome any initial differences.