I'm the family cruise editor here. Often parents will call the reservations center of the cruise lines and the res agent will say that children in diapers can play in the youth room with a parents' supervision. However, when the parents get on the ship, the youth counselors generally do not allow this. I think it's because they feel it will be disruptive to the organized youth activities they have going on in the room.
Also, most of the cruise lines do not allow diapers even in splash pools for health reasons. However, I have found, as have many readers of this site, that generally there isn't anyone standing at the pool checking to see if kids are wearing diapers. So it's really your call...
I hope this is helpful. Your toddler will probably be pretty happy riding glass elevators
and just running around. I have a son who is 17 months and he likes to wander around and check everything out. FYI...NCL's youth program starts for those who are 2 years and older.
I hope this helps. Feel free to ask any add'l Q's.
Smooth sailing,
Luisa Frey Gaynor