Concourse Steakhouse is a TS, not CS restaurant so that comment doesn't apply for your question.
Using CS for a breakfast meal you can get two beverages. We usually got a bottle of Dasani and either juice or chocolate milk (5yo in the decision process). We would take the water to the park and drink the other with our meal, often still having enough left to put in the fridge for later. By the way, I never saw a bottle larger than 24oz when we were there Aug 30-Sep 4th. Our home was CBR, but we stopped in the CS locations at the Poly and WL too. Never saw anything bigger in the park either. During our food court meals I often drank complimentary water from the fountain. That water is filtered just as Dasani (Yes Dasani is not Spring water).
We used a few snack credits for beverages (water and Powerade) and had enough for the treats we wanted as well. To me the CS meals are the hidden jewels in the dining plan. Portions are usually big enough to share, bottled drinks are included and you get a built in snack by selecting a dessert item.
We also had a small stash of bottled water from home (6 bottles or so). I walk when I golf so I always keep bottles in that bag. I just threw in a few extra and they travel just fine.
Your question was about water, however I did not see many "big" sized items in the CS places. We bought some Entenmann's products and saw chips and pretzels, but I didn't see any 2L soda, big boxes of cereal at the Poly, CBR or WL and I did a quick scan looking for those items because of things I've read on the boards. Not sure if they were tucked away for
Free Dining Period or if there is just a change.