I'm pretty sure princess will allow you to bring a small, soft-sided cooler that holds about a 12-pack of either soda or water. I often buy a tall bottle of water or two in port during cruises and they never stop us from bringing them back onboard. I doubt they would care about soda from port either.
I am the editor, but I also speculate, ask questions and play devil's advocate. I reserve the right to change my mind.