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As there are no antenni sticking out of the Atlantic Ocean, the answer is NO your mobile will not work. Satellite is used to telephone on board ship but it is VERY EXPENSIVE. Check with Cunard for their arrangements. If you are going to New York then the 'world' phone will work though you only need dual band there.
I disagree with Macro, In NYC you would need to use a TRI-BAND mobile since the yanks are on another system ( as usual ) . Regarding Mid- Atlantic, if you were on the Grand Princess for example your mobile would work all the time through their own system ( check costings ) however On the QM2 the Cunard cheapskates don't do this so that you need to call from your cabin at a silly price.
Best alternative is to use the e-mail facility in your QM2 cabin it's only about 50 cents per time - much cheaper than the telephone for keeping in touc.
Thankyou for replies . I am hopeful as i have a triband...if not its www.