Inverters don't depend on wapda voltages to trip a battery once its full. The charging amps depends on wapda voltages Higher the voltage higher the amps. Even then the UPS/inverters have certain tolerance among fluctuating WAPDA voltages.
Easy method to see if you need a stabilizer or not is just to check the amps with a DC amp meter. If your UPS is charging the battery at 16 or say 17 amps at wapda voltages of 175volts. And not decreasing charging amps even at 170 WAPDA volts. Then clearly you don't need the stabilizer.
We hook up stabilizers so that ups/inverter get proper voltages for charging since some ups/inverters have low tolerances among the fluctuating WAPDA voltages they even stop charging below 180 volts. Now thats where you would want to install a stabilizer.
By the way, according to an expert, to install stabilizers at these high amperes you might need a big beafy stabilizer, say 5000 watts.