Compare the charge of those pulses, to the charge stored in the battery.
You'll find it's utterly negligible, at least unless the 8/20 is scaled to simulate direct lightning strike... in which case you have bigger problems than mere acid spatter.
In addition to the usual, slow, battery behavior, batteries also have quite large capacitance at shorter time scales, due to the combination of electrode area and electrolyte dielectric constant. Ionic surface layers store a fair amount of charge by themselves.
Also, for high enough currents, the chemistry won't matter very much as the sheer voltage drop across internal resistances (mostly the electrolyte) dominates; in this regime, the battery doesn't act so much as an absorber, as a resistor.
Large peak currents probably have implications for disturbing (stirring up or mechanically shocking) the battery structure itself, but other than that, they're very much just big lumps of metal and other bulk chemical stuff that doesn't give a rat's ass about tiny electrical stimulus.
How/WHY are you generating 16kv discharge pulses?
And what's with the 6kv 8/20uS pulses? And why are you using a LC filter? LC filters are mean to deal with AC power not DC power. In a DC circuit an LC filter isn't going to significantly limit the voltage or the current going to or from a battery.
Nothing that you said makes sense in a battery circuit.
16kV easily arises from plain old carpet. 8/20us pulses are typically used to simulate induced lightning transients.
ESD is trivially handled by a battery as the charge is minuscule (16kV * 330pF = 5.3uC = 1.47 nAh), but more importantly, the connecting wires will have significantly more impedance (stray inductance or whatever), being that the frequency content peaks in the 10s to 100s MHz range.
I don't know what surge would be doing there. Surge is most often a mains power test, and a battery has absolutely no business connecting to mains. Surge can also appear on long wires (mains wiring just happens to be the most common example), but I don't know where you'd be running 12V or so over very long distances (e.g., facility wiring, alarm systems, telco, automation and control..).
Tim