He'll be fine! As long as he has a jacket or a tie, it'll be fine. Many times when I cruise I don't want to hassle with the weight of a jacket, so I'll just wear a tie and even on Holland America or Celebrity, which are a bit more formal than RCCL, I've never had any problems.
So tell him to relax and enjoy the cruise!
Travel Agent/Cruise Specialist w/12 yrs exp and 47 Cruises on 11 cruise lines! Favorites: Paul Gauguin - Tahiti: Uniworld River Cruises - Europe; Celebrity Solstice-class ships; Holland America - 12-nights Baltics & Russia; RCCL - 14-nights Greek Isles, Turkey, & Croatia; Holland America - 14-day Alaskan cruisetour; 10-night Canada/New England cruise; 21 days Hawaii w/7-night NCL cruise; Oceania - 25 days in Asia; more than 3 months touring Europe by train. And many all-inclusive resorts!