Health, shmealth, people! It's sugar - it's not supposed to be good for you! Brown rock sugar isn't about health, its about yummy delicious goodness that turns an ordinary cup of tea into a luxurious interlude redolent with Eurpoean savoir faire!
Seriously, while brown rock sugar is simply a carmelized form of white rock sugar, it is truly delicious. The taste is different from white rock sugar, because of the carmelization, and while I imagine that it would be overpowering in a green or white tea, it adds a depth of flavor that really compliments the stronger oolong or black teas.
FYI - Teavana claims that their brown rock sugar is "unprocessed." However, the caloric information for their sugar is identical to that of white table sugar, and does not match the calories of the less processed turbinado or demarara sugars. In addition, I have not found any method of rock sugar production that uses non-white sugar. The sugar, plain or carmelized, is boiled with water into a syrup, and then the water is slowly evaporated off to leave behind the solid crystals.