There seems to be some debate. Coca-Cola does indeed claim (not just at Disney but also at World of Coke in Atlanta) that it sells Beverly in Italy, but allegedly "no one from Italy has ever heard of it."
I did find another web page that claimed that Beverly *was* (as in used to be but no longer is) a beverage that Coca-Cola marketed in Italy to try to tap into the popular aperitif market--there are lots of bitter fizzy non-alcoholic aperitifs in Europe, Chinotto and Crodino are two of them. So maybe it's more like Beverly is a Coke rip-off of a type of beverage that really is popular in Italy (like, say, Pibb Xtra [formerly Mr Pibb] is a rip off of Dr Pepper).