We're on the NCL Jewel non-Nick theme cruise last year and there're plenty of children-oriented events, with 500 kids on board and it wasn't even official school break or summer sailing. The sailing after us was a full Nick cruise and crew members told us they will be getting 1,000+ children onboard for a full scale themed cruise.

In either case, there're special theme-breakfast in a dedicated MDR with photo ops ($$) and kids-only event in the Lounge, activities in the kid's center, etc. and decorations on the ship (plus the gift shops with sale items) to reflect the pitch.

Check the NCL website & you can online request a PCC to call back with specifics, as s/he will be happy to research the info & call you back to "assist" you with the booking/reservation.