Maybe, but probably not. Someone else has already linked to some other AskHistorians threads discussing this, so I'll just add a couple of primary sources.

In a famous passage, the Greek biographer Plutarch, writing around AD 100, says in his "Life of Agesilaus":

I by no means assent to Demaratus of Corinth, who said that those Greeks lost a great satisfaction that did not live to see Alexander sit on the throne of Darius. That sight should rather have drawn tears from them, when they considered that they have left the glory to Alexander and the Macedonians, whilst they spent all their own great commanders in playing them against each other in the fields of Leuctra, Coronea, Corinth, and Arcadia.

Plutarch was a great admirer of Alexander, so it is significant that he can speak of the glory of "Alexander and the Macedonians" as something that the Greeks, by contrast, had lost through their civil strife. Moreover, if the Macedonians perhaps became considered more and more Greek over time, their Greekness would certainly have been established by the time of a relatively late author like Plutarch, who nonetheless contrasts the two.

Herodotus, at a much earlier period, tells us at Histories 5.22 that Alexander I (not Alexander the Great, but his ancestor) wanted to compete in the Olympics, but was originally turned away on the grounds that he was a barbarian (that is, not Greek); he was permitted only when he "proved" according to a somewhat shadowy genealogical tradition that the Macedonian kings were of Argive origin. This shows that there was an immediate assumption that the Macedonians were not Greek. Alexander I was allowed to partcipate because he argued that he was by descent not Macedonian at all, but Argive. There was thus a tradition that, though the Macedonians in general were not considered Greek, the Macedonian kings may have been.

You may be interested in this thread which conveniently links to several other discussions about what constituted being "Greek".