Two years ago I tried fermenting Tea with Trader Joes Irish Breakfast Tea, two (maybe three) pounds of turbinado sugar and a generic champagne yeast (i think). It was an off the cuff experiment to make 5 galls for under $10, so I didn't take notes on brew day. I never went back and wrote notes because it turned out so terrible. The yeast annihilated the turbinado sugar and left me with highly alcoholic and undrinkable bitter tea.
After thinking about this for two years, I think the key would be either back end sweetening or using Splenda in addition to the fermentable sugars. I hate the taste of Splenda, but it might be different in this kind of situation. I never thought about trying to make this without carbonating it at some point, but it might be worth giving flat a shot. Maybe something to try would be back end sweetening with a low sugar lemon juice and Splenda or sugar? If you put it in the fridge immediately the yeast should stay dormant.