This would be somehow equivalent to applying high frequency indeed...
My point is! High voltage actually can do nothing to water in a burst like this having extremely low current! a capacitor is known by its major characteristic it can not change voltage instantly but it can change current instantly. For example you discharge a capacitor thru a resistor... At the instant the capacitor and resistor are in a close circuit the initial current is going to be maximum since voltage is pressure and resistor sets the time needed to the capacitor discharge.
So high voltage don't really goes thru the circuit its indeed across the spark gap and at the cell only few volts if so...
An inductor can change its voltage instantly but it can't change current instantly likewise.
If it was a capacitor discharging and somehow the spark gap is improved by making the contacts actually touch each other at every spark, than things could be different! Since high current can flow to charge up water rapdilly enough! But thats only considering ideal water with ZEro ions in it.
For real water is impossible to apply such high voltage fields without restricting the damn amps like meyer told us about!