Perez recast the Amazons as being completely multi-ethnic, women from all over the world reborn after dying a violent death.
However, since the beings who granted them new forms were the Greek Pantheon, and they have always based their style on Classical Greek themes, I'd say yes, they historically count as being Greek AND Amazon.
However, they would no longer be Greek nationals, as Themiscyria is recognised as a sovereign nation with it's own UN representatives and ambassadors etc. So I'd say it was akin to a Greek inspired colony which achieved independence a long, long time ago.