It all depends on what you mean. Ethnically? As in, from a genetic point of view? Yes, modern Greeks are largely the same as classical Greeks. I know wiki is generally a pretty bad source on these sort of things, but the 'Greeks' article, specifically the 'Modern and Ancient Greeks' bit, is very well sourced and supports the position that Greeks of both time periods are largely of the same ethnic lines.
Honestly, France is mostly ethnically Gallic, Italy still has large Etruscan ethnic populations, etc etc. 'Invasions' are rarely so in that they they rarely actively eliminate entire ethnic groups and supplant them with another. What actually usually happens is a period of political and linguistic dominance. Sometimes this is permanent (Egypt, North Africa, Finland), sometimes the original language re-asserts itself (Greece itself, Spain after the Visigoths, etc), sometimes you have a fascinating synthesis (France, post-Norman England, post-Muslim Spain), but mostly the actual genetic pool of the area experiences little more than an infusion of new genes. After the establishment of civilization in an area, it actually becomes really hard for even a politically dominant ethnicity to assert itself successfully over an extant sub-polity.
That's, to mention, why modern genocide is so disgusting. No matter how many people tell you about how common genocide was in the past, it actually wasn't. Yeah, the Romans would kill all the men of a city and sell the women and children into slavery; yeah, Assyrians would kill a whole lot of people at random to spread fear; but ultimately concerted efforts by a government or state-like organization to completely eliminate another ethnicity are surprisingly rare in history.
I guess the point I need to make is that the Germanic invasions of the Roman Empire which 'Teutonized' Romania generally involved tribal groups numbering in the low thousands, rarely above a dozen or two thousand, invading an area populated by tens or hundred of thousands, or even millions of people. Slavic tribal invasions into the Eastern Roman Empire tended to involve similar numbers. The 'hinterlands' the Slavs eventually came to dominate in the Balkan peninsula remained, before and after, the invasions as low-population intensity areas.
Linguistically? There have been changes, of course, but they're largely similar in the sense that there are clear lines of descent within the Greek language sub-family.
Arguments like Fallmerayer's are examples of the 19th century's extreme obsession with race and racial characteristics. They believed that, had the 'modern' Hellenes of their time not been direct descendants of the ancient ones, they could not achieve the same level of civilization. It's all really nonsense with no place in the modern mindset.