For what I understood, you control the servomotors with a pulse coming from the analogue pin right?
My battery voltage is constantly droping and I would like to be sure, it won't damage the precision of the mouvement made by the servos over time right? Because it's only directed by the pulse and nothing else.
Arduino doesn't strictly have analog output pins, although the PWM pins give pseudo-analog with analogWrite().
But that's irrelevant: the servo library uses digital pins which don't need to be PWM "analog" ones, to send the controlling pulse with servo.write().
That said, I don't understand the part of your question about damage.
I think the real concern should be why the battery voltage is constantly dropping, and you should be looking at a better supply if it's going below what the servo needs.