We went on the Pride in April and saw a couple with a dolley taking 2 cases of diet coke and a case of water on. They seemed to have no problem getting on with it. The water is 1.95 for a 12 oz bottle and 3 - 3:50 for a larger one. We drank the water from the lido deck. They have water fountains and ice machines set up and we just filled up cups and took them back to our room. I also don't think that you will have any problem putting some in your luggage.
Have a good trip!