The historical view is that there is no simple answer; it depends on whom you ask, and when you ask them. The Greekness of the Macedonians was contested for both cultural and political reasons. I wrote about Macedonians and Greeks in more detail here and also on the historical controversy here.

For me the answer is a resounding yes. As the previous comments and links rightly point out there is a lot to unpack when answering this question. I won't repeat what has already been said, just add my own thoughts. A group's collective identity is constructed over time and not isolated to one location. It would be a mistake to interpret that reality as meaning that we cannot connect ancient and modern identities. It is actually very similar to how most people don't understand commercial DNA tests. Just because a company interprets your DNA as French, even though your genealogical records point to Germany, doesn't mean that studying DNA is pointless. It is just one tool that can be used to help build your genealogical records. Yet, if you don't understand sample populations, haplogroups, etc. you won't be able to interpret your results accurately. In the same way we can connect modern and ancient Hellenes because there is a large degree of continuity (cultural, genetic, geographical, etc.) that shapes our group identity. Greekness, like all ethnicities, is not absolute. It never has been and it never will be. Historically, we have places like Cyprus and Sicily which were decidedly not Hellenic but became Hellenic as their "native" culture fused with that of Aegean traders, soldiers, and settlers. The idea of classical mainland Greeks being "more Greek" than other Hellenes is ridiculous. Its only usefulness is in exposing the historical bias that exists in favor of classical Athens. This probably has more to do with the availability of literary evidence than anything else. What does this have to do with Macedonians? Macedonians were a group, or subgroup of Hellenes just like Spartans, Ionians, Tarantines, etc. Their culture (most crucially religion, ancestry, and language) placed them firmly within the spectrum of the Hellenic world. The fact that historical and contemporary writers have objected to the Hellenic character of Macedonia is indicative of opposing expansionism in the former, and an attempt at modern nation-building in the latter. While politics can certainly affect how groups build their own identity, they are less important than the actual cultural and genetic considerations that are involved. To summarize, I agree with much of what has been said by others here and in the links. On the other hand, this leads me to the conclusion that the ancient Macedonians were undoubtedly Hellenic. I don't think that I am overstretching by saying that the overwhelming majority of classicists agree with me on this.