In an early stage of the Ancient Greek language there was a semivowel called wau or digamma (double Γ, because of the F-like shape). It was positioned between the ε and the ζ.

The wau was still in use when Homer composed his Iliad and Odyssey. But by the time they were written down the wau had disappeared from the Greek alphabet. Many apparent irregularities of epic verse (e.g. hiatuses) can be explained only by supposing the semivowel W was actually sounded.

This proves the W's always got an ambiguous role, being neither fully a vowel nor a consonant. And even though in most cases there's a clear tendency towards one of the two, it still is a semivowel and most likely will remain one forever.

Thus we can conclude W is never a vowel.