One deep discharge didn't ruin them if they were is decent condition before that. Those GC2 golf car batteries are pretty rugged. Lead-acid batteries have a limited number of deep discharge cycles, though, and every major discharge like that reduces the amp-hour capacity a little bit. Rarely ever will it simply kill them, though.
From the converter/charger perspective, badly discharged batteries will look the same as internally shorted batteries and the charger will either shut off completely or "pulse" the charge until the voltage comes up enough for normal charging to continue. The charger gives it a brief burst and then shuts off to avoid overloading, then it tries again a short while later. Eventually the battery voltage and charge level builds up enough (typically around 9-10v) for the normal bulk-absorption-float charging cycles to operate continuously.
Since those are flooded cell batteries, check the electrolyte level in each cell and top up with distilled water if needed. After about 24 hours, turn the charger off (or disconnect shore power) and measure the battery voltage with the charger off to see if the batteries reached float charge stage, about 13.6v. If they did, they are very probably fine.