Will a dentist use anesthesia before a filling if they aren't drilling?

I had a filling pop out while eating taffy a few days ago, and need to get it replaced. The dentist said there's no new cavities and they just need to re-do the filling process. I have a serious needle phobia and am curious as to whether I will be injected with anesthetic before the procedure, or if it can be skipped when drilling is not required.