Is it possible to bring, say a special bottle of wine or two, onto the cruise ship with you?

Yes, if you inform NCL prior to arriving of your plans. They will probably charge $15 per bottle corkage fees.
Otherwise, bringing your own alcohol is greatly discouraged, NCL will confiscate all your alcohol and will not give it back until the end of the cruise.

You may also call NCL and ask to have a bar set up in your cabin. I believe the charge per bottle is $55.00 on the Star, but request it in advance, as ordering it when you are sailing will be more expensive.