Absolutely not. The category "white", with its triple-barrelled connotations of skin-colour, ethnic category, and eurocentric opinion about what constitutes "civilisation", only goes back to the 1600s: a convenient (and detestable) example is in Ness, Complete and Compendious Church History (1680), which in chapter 3 discusses Satan's plot

To corrupt the White Line (the Posterity of Seth,) and to make them as black as those of the black Line, the Cursed brood of Cain.

Even the ancient Greeks, whose culture was certainly appalling in many ways, were not guilty of this particular kind of evil hatefulness. It is to be hoped that the kind of negligent racism you describe should always be called out and promptly criticised.

In addition, there is no reason whatsoever to think that Classical-era Greeks are a significant component of the modern European genetic make-up. Even if there were, your "friend" might be interested to know that nearly all of the most celebrated ancient Greek scientists and scholars of antiquity were born and lived in Egypt and Libya, not Greece.