Yes they buy sugar. Two kinds, and three sugar substitutes available if I recall. The tea is a post mix fountain type they have in the casual serve yourself restaurant on Lido deck.
I am pretty sure, but not certain as I didn't order it the last few years.. That the tea served in the formal dining room is fresh brewed. It is un-sweetened though.
My wife and I are not big soda drinkers but I still purchase the cards. It is true that sometimes the deck staff is not very happy about the soda cards but they will still fill your order. Sometimes, there is no substitute for a cold Coca Cola... especially, with a splash of Caribbean rum.