kombucha needs air, and I don't think it hurts to have a scoby creating that loose seal around the edges of the jar with the top of the scoby mostly exposed to air. I did that for nearly three years without any problems. My batches always were full of wee little bubbles of sparkling goodness
I'm not all that aware of anaerobic fermentation and kombucha. I do know that it will cut off certain processes and cultures from flourishing within the brew after a short period of time. Some people do play around with anaerobic fermentation of kombucha to increase the alcohol content, but it's at the cost of the full health benefits.