No to the drink refill stations, and I don't recall ever seeing it at CS restaurants. Only places I've ever seen that is club level lounges and bars. Not even sure about TS restaurants but most of them have bar service so you'd be OK with those probably. If you find a place where there is a bar, you could get some there. All of the drink stations and CS have filtered water (not bottled at the drink stations) and you could probably buy Perrier at the resorts.
There are bars you can visit in all parks except MK.