Electrochemical cells (batteries) are not passive components, instead they're active charge-pumps having internal feedback effects which produces a relatively constant voltage at the output terminals.
If an external field impinges on a battery's terminals, this will produce a temporary small change in potential on the terminals. But the battery then actively responds with a very small, brief current which only persists long enough to restore the potential across the terminals to the same value it had before the external field was applied.
So, if you wave an electrically-charged balloon back and forth around one terminal of a D-cell, a very small AC current will appear in the battery terminals and within the electrolyte: exactly the current needed to maintain the ~1.5 volts of potential difference across the battery terminals.
To understand the details of battery operation, look into the physics of "half-cell" electrochemistry. Below is a very brief ELI5 version.
A metal plate dunked into fluid electrolyte will rapidly dissolve: rapidly like sugar or salt in water. But as metal atoms corrode away, they each leave behind one or more outer electrons in the metal's "electron sea." Quickly the metal becomes charged net-negative, and the electrolyte becomes charged net-positive by the population of metal +ions in solution. Electrostatic attraction tends to pull the metal ions back towards the opposite-charged metal surface, while thermal vibrations tend to make the atoms diffuse away into the electrolyte. When the "force of dissolving" equals the electrostatic attraction, the corrosion process slows to a halt. There will be a constant voltage left between the electrolyte and the metal. If an external circuit is used to increase this voltage, then the metal ions are forced back to the metal surface and so we have "charging a battery" and also electroplating. If an external circuit should reduce this voltage, then more atoms can dissolve from the metal surface and so we have "discharging a battery" and also electrolytic corrosion. Note that a single "battery" cell consists of two different metal plates connected by a common electrolyte, and the voltage on the terminals is simply the difference between the half-cell voltages which appear in the thin region between the electrolyte and each metal plate. Note that all components are conductors, and the entire "charge pump" is located in a molecules-thin layer adjacent to each metal surface.
A battery is a chemically-fueled, constant-voltage charge pump.