How will the performance (XZ plane signal) drop if a battery encroaches on the lateral space adjacent to the antenna. Would this kill the performance or only slightly reduce the signal? Perhaps it would only create a small localized dead zone in the 90/270 degree orientations…?
On average over all directions it’ll reduce performance and it will increase directional variation in performance.
Directions close to the line from the antenna to the battery will probably suffer from reduced sensitivity/range. How badly would depend on details of the battery and how it’s mounted.
Other directions are harder to predict, you’ll probably get better performance in some directions and worse performance in others. How much different and in which directions is anyone’s guess.