Raw sugar vs. refined sugar in making kombucha
Absolutely you can.  I typically use a Turbinado sugar when making mine because it's what I buy in bulk and because I like the robust flavor.

In my searches, I did come across this article indicating that you shouldn't use such raw sugars because they're more difficult for the scoby to digest, but as long as you start with a healthy one you should be fine.  Maybe just don't go as far as using a brown sugar, or something very raw like muscovado.