Do kids clubs provide beverages?
I had to ask my daughter because honestly, I have never payed attention to this.
There is usually a water fountain in one of the rooms (She said Aquanauts, but I'm not sure if its the same on every ship) They are allowed to go get water if needed.
Other than that, they do no provide beverages in Adventure Ocean. I imagine this has to do with all the kids and the risk of spills. It would probably very quickly make the room very dirty and sticky.
The Royal Tots and Babies Nursery does provide food and drinks to kids 36 months and younger.