Yes.. I have seen many people bring children/babies on cruises. It really depends on the cruise line. Some are more family friendly then others.
Your son and wife will have a very family oriented cruise. There is no babysitting for a child that young available on NCL. They do have sleeping set up for children but its not a full crib. I don't know what size cabin they will be having but that does take up space.
You can take the baby in the show.
Children who are not potty trained can not go into pools even with swim diapers. If there is a choice, it would be nice if son and wife have a balcony cabin so they can enjoy together time on the balcony while the little one is sleeping.
I hope you have a fantastic cruise.