Nope, not really. The current official form of modern Greece is based on previously existing ancient varieties, and in some cases there's a fair amount of mutual intelligibility, but they're still not quite the same, and you'd have some difficulty making yourself understood clearly were you a modern speaker who suddenly found yourself in possession of a time machine.

We actually have flaired users here who are proficient in different forms, so they can give you a specific history of the different varieties if you're interested. Otherwise Wikipedia isn't a bad place to start.

Languages change considerably over time, even despite many people's best efforts to prevent it. Even cases where a language has effectively died and then been revived (Hebrew being the poster child of such efforts) end up changing considerably from their earlier forms. You can't really prevent language change, and at best efforts to do so will only slow it down.

It's safe to say that no modern natural spoken language is the same as it was a thousand years ago. Certain features of certain languages or dialects may be considered more conservative than those found in other related dialects, but still, none are actually the same across the board.