We would definitely still have tinnitus because it results from any kind of damage/dysfunction somewhere in the body. If it were a memory thing, then anyone who has ever had tinnitus would have it forever and that obviously isn't the case - talking about people who have it for a few hours after a loud event or people who have it from an infection and for who it goes away after say, two months as the infection clears up.
However, if we didn't know any better then we would interpret this as silence. Not quite the same, though.