No, I'm not saying anything in Italian just to get a cup of coffee. You will respond to small, medium, or large or if I'm feeling especially incredulous, simply 'the middle one' or the 'cheapest one'.
Nor will I refer to you as some 'Barrista' which is clearly a made up job title.
And when I order a double espresso you respond 'double espresso', thus successfully verifying what I ordered. I'm not referring to it as some preposterous Euro-centric vowel laden warble.