I don't have balance issues, but didn't before either. I was certainly worried about how the surgery would affect my mobility in the medium to longer-term. But was only an issue in the very short term...
The first week was tough (but then again, i spent it horizontal in the hospital. i only got up to walk, with a walker, a few times, and it was certainly tough, but that was only the first week!), and certainly felt vulnerable for a good month, but i would rate my balance at at least 95% pre-surgery now (and would have said the same at 3months post). The only time i really sense anything different is when i turn my head while walking fast, say to see if the bus is coming. I think i misstep a bit, but no biggie. I came home from the hospital with walker and ditched it the next day (luckily we have a small house, bungalow). But first month is probably a little tough on all... they do cut your head open after all (and the thought is MUCH scarier than the reality).
I think this one of those things that is different for everyone, but balance issues are not a given, even with a cut nerve. Hopefully the doctor can give you some indication of what to expect. You do want to be prepared for anything.
good luck,
Trish