Good question...I had the same question for my doctors. Yes, I am totally deaf on the AN side (confirmed by my audiologist) as the hearing nerve was too involved with the tumor when it was removed. The only thing I hear is the tinnitus on the AN side.
My neurotologist explained that sometimes the brain (in absence of receiving normal sounds to transmit) will make up its own noise in the form of tinnitus. I was hoping that with the hearing nerve being totally shot, the tinnitus would go away, but in my case it actually got a little stronger after surgery. However, I can block it out most of the time and it doesn't usually bother me or affect my family or work life. The tinnitus does tend to get louder in noisy environments, at least for me.