Kombucha does contain yeast, but the yeast is a different strain than candida and competes with it. It is similar to trying to fight a bacterial infection with probiotics.
Regarding the caffeine; virtually all of the Sugar and caffeine in kombucha is converted into other compounds. That is what feeds the culture. That said, I have heard of people making kombucha from mountain dew, and virtually anyting. Once you have a good supply of mushroom babies it would be fun to see what you can make kombucha out of. Just make sure to let it go long enough (pH papers available at any pharmacy are helpful; you want about 2.6) so the Sugar is consumed.