We have been on several Princess cruises and they do have themed nights, ie Italian, American but these are related to the evening menu. The waiters do dress accordingly, but I have never seen any passengers do so. Enjoy your cruise.
They have an island party on the lido and riveria decks. Music, dancing, games and lots of people dressed in 'normal' and island themed clothing. This happened at least once that I recall on Sea Princess during Easter 2008 cruise. You don't have to attend it, of course. I didn't. There was plenty other things going on, on the ship too.