It has been tried, but I think the results are less than what you would hope for. The reason being, when tuning the servo, trying to create an optimum PID filter, the mechanical backlash amount interferes with the stability that you can achieve in the PID feedback loop. This is because a tiny error in position of the axis is not proportionate to the motor position, ie., there is the inevitable dead spot where there is no response even though the control circuit has attempted to bring the motor into position. Then, all of a sudden after the backlash space has been traversed, small increments in motor position do start to matter.
It is also the case that a tool in the cut can exert enough force when climb cutting that it pulls the machine table across the backlash space, taking a heavy chip, or leaving a mark when an axis direction is reversed during circular motion.
Mechanical backlash should be eliminated with better mechanicals, the electronic compensation has its limits. It will work to a certain extent, but the settling time for the axis to reach true position is much longer, and so the best tuning settings will be kind of spongey, instead of crisp and distinct.