We also don't drink alcohol and have had this issue before with the drink packages that come with the various promotions. Sometimes they'll do it, sometimes they won't. But I've only ever been successful by asking guest relations on the first day. Bringing information to support your case is probably a good idea, as was mentioned previously.
I had not heard of this new "Zero Proof" package, though. Considering how quickly younger people are giving up alcohol I've been waiting to see how Celebrity would react. There are only so many times you can turn down free champagne before you start wondering if you're getting your money's worth.