Of course and that’s the polite thing to do. Bu when a customer orders it in the correct pronunciation, the server shouldn’t confirm the order by mispronouncing it. Happens a lot. I don’t expect every American to pronounce it correctly but if you are working in an Italian restaurant, I think you should (and I’m not talking Olive Garden 
).
Any of the comments made here can be a “pick your battles”, @skieurope. They are all small potatoes nitpicking but that’s what the thread is about.
Nobody knows that Cannoli is actually the plural - the singular is Cannolo, but we all ask for a Cannoli at the bakery counter. I am that person who pronounces all Italian foods the way I was taught in an Italian American household. So for ricotta, I cringe when people say ricata and for mozzarella, when people say motzarella. I am prone to getting rid of the final vowel anyway so I may say ricot, or mozzarel or just mozz.
But of course. One cannolo is never enough.
Non-native English speaker here having a headache from just reading this thread. How do you guys manage to communicate at all? 
@kiddie I’m Italian too but the opposite of you, cringe when people (NY/NJ Italians mostly IME) shorten ricotta and mozzarella saying it like ri-gut and mooz-a-rel. Different strokes LOL
I’m not Italian, so when I moved to a very Italian North Jersey town many years ago, I was very confused when people referred to pasta fazool, or gavadiel (Pasta e Fagioli, and cavatelli).
On the other hand, my H’s stepmother, whose Italian family ran a well-known Italian restaurant in the Village, introduced me to what she called “Bru-SHETT”.
This is neither regional nor language based. Just idiosyncratic. I just can’t say the word “signal.” It either comes out “single” or “sig-a-nal.” My spouse has been amused by that for years.
I also neither hear nor can say the differences between fairy and ferry, or Shari and Sherry, or Mary and Merry. No amount of anyone’s trying to teach me the difference ever works, because I truly can’t hear it. My spouse always teases me that I say Mary Christmas, and is it Joseph and Mary Christmas?
I can hear the difference between marry and merry, but I have always pronounced Mary the same as merry. It used to drive my mom crazy because that was her mother’s name, and she couldn’t understand how I don’t hear it. She said something like May-ry. But to me, Mary and merry are pretty much the same. (Well, I guess if I think about it, I can say “Mare-ry”. But if I don’t concentrate, it’s Merry.) Marry is different.
To be fair, while dropping the last vowel occurs often with Italian-Americans around NY/NJ, it’s not uncommon in the old country either. Like English, Italian has regional variations. While all syllables are generally pronounced in standard Italian (and most northern dialects), some regional dialects, particularly in southern Italy closer to Sicily, often drop the final vowel.
Italian has many dialects that can vary significantly… None of the Italians I interacted with as a child spoke true Italian. It was a joke in my household that my father had taken Italian in school but my mother had learnt Italian from her parents and their Italian was completely different. Most of my family and neighbors were from southern Italy so I heard Gagootz as a child and not Cucuzza which is the real word for Italian squash.
Cucuzza is actually a specific type of squash. The Italian word for squash in general is schiacciare.
We spoke true Italian at home but OMG was it tough going to see family in Italy. I could get by with Venetian dialect because that’s all my great grandmother spoke, but forget it when we went down south to see the other side of the family. It was like a totally different language.
Whenever I try to pronounce the word “lawyer”, it always comes out as “liar”.
Some of the Italian-Americans at the gym said that when they visit their Scicilian relatives that they think it’s funny that they basically are speaking with archaic dialects where it’s much more common to drop the last syllable.
When I was in middle school, I had a classmate from Australia who pronounced Mary, merry and marry differently. His word for jeans was dungarees. Sunglasses were sunnies, and chinos were khakis.
^^Other than the sunglasses, that’s my mother, whose name happens to be Mary, from the ‘Noth Showa’ of Boston.
Mary, marry, and merry are the same to me. I can hear that some people say them differently, but I struggle to replicate the sounds.
I do distinguish between pin and pen, and aunt and ant.
I say khakis too
Khakis is not a uniquely Ozzie term. Although in Boston, “khakis” and “car keys” sound the same.
Have discussed this before, but my freshman year roommate , from Boston, asked me, shortly after we moved in, if I was going to the potty. I wondered why she was asking about bathroom behaviors. Apparently she was talking about an upcoming dorm party.
Definitely grew up saying dungarees and sliding pond.