Well kind of, in the last century 1900-2000 in Australia, Greek and Italian immigrants weren't considered "white". The only immigrants that were considered white were from the UK (and maybe France, Germany, and the Nordic countries).

There is a semi-derogotary slang term used for people of that descent in Australia, but it escapes my mind at the moment. Nevertheless the people immigrated from Greece and Italy and made a significant impact on Australian culture.