I don't think there's a clear-cut answer here. There are so many factors in play with how languages evolve over time that you can convincingly take it into either direction.
While most answers seem to suggest that the two groups wouldn't understand each other, you can also find real-life examples supporting the other side:
Ancient Greek being intelligible to modern Greek users
Greek is considered to be the oldest recorded living language, with ~35 centuries worth of written artifacts. While the language underwent evolution over the ages, the changes are said to be comparatively minor, due to lucky historic circumstances (Roman Empire was effectively bilingual, Byzantine Empire was clearly more Greek than Latin).
I've seen people claiming that while Homer (30 centuries old) might require a dedicated study, Thucydides's writings (roughly 25 centuries old) are generally understandable to modern Greek speakers without any special preparation.
Still, Wikipedia quotes one source saying that "Homeric Greek is probably closer to demotic (modern-day Greek) than twelfth-century Middle English is to modern spoken English."
Friar Julian's expedition
Present-day Hungarians are descended from Magyars, a nomadic tribe that settled in Carpathian Basin in late 9th century, converted to Christianity and established the Kingdom of Hungary.
Fast forward to 1235, one Friar Julian left with a group of Hungarian monks in order to find Magyar tribes that were supposedly left behind in the east. He found them and despite the 300-400 year gap, during which there was virtually no contact between the two groups, was able to communicate with them in his own tongue.
Interestingly, other than the language, the culture of both groups went two separate ways - Hungary was already an established feudal European country, while the eastern Magyars were likely Tengrist and led a lifestyle similar to their shared ancestors.
So if you want your two groups to be able to understand each other - it's something that can plausibly happen.