Are large electrolytic capacitors necessary in a servo system that doesn't need to be precise
Typically, any feedback system requires capacitors, so that small fluctuations in the power supply due to movement of the motors do not create another unintentional feedback path. In this case, the charge lost in 1 discharge cycle of two 250uF capacitors is minuscule compared to your battery capacity: 250 uF * 5 V is about 1.25 mC, by comparison 1 mAh (where most batteries are on the order of thousands of mAh) is 3600 mC. Therefore, a typical 1000mAh battery can theoretically support many million charge and discharge cycles of your caps. 

Not having capacitors may very well reduce your battery life, if small fluctuations in the power supply cause noise in your servo feedback readings and therefore cause the motors to move unnecessarily. Powering up the motor (even for a couple of milliseconds) is likely to waste magnitudes more energy than charging and discharging the caps.