Can servos have a true neutral gear?
A servo-motor will not be fully "in netral" in the sense that you mean unless a specific mechanical neutral arrangement is used. However - 

A servo-motor may be geared or ungeared.


An ungeared servo motor will provide relatively small counteracting torque if the drive coils are left "open circuit".
If it uses a permanent magnet field rotor and the stator contains "magnetic material" there will be some losses due to eddy current effects. An "ironless" stator using wound coils only will have relatively small losses and thus impeding force. The rotor magnets passing the copper windings will induce some eddy current losses.


ie overall there will be some interaction but it will be small compared ton the torque or power usually exerted by the motor.


A geared or belt driven servo is liable to exhibit more losses and more drag than a direct drive one. In extreme cases a gear train will not "overhaul" and will be unable to be turned by any amount of rotational force. This is a very well known attribute of gear drives and will be designed for accordingly.


If a "clutch" mechanism is provided any load produced by the motor will be a function of the clutch design and may be arbitrarily small 'by design'. For example, using a meshed/unmeshed idler gear will provide an essentially zero drag or loss design.
In some systems it is usual to use an electromagnetic clutch with an electrically activated coil. These can have minimal losses (mainly air drag between rotating and stationary parts.) 

A common use of such a clutch - although not a servomotor application, is the electrically operated clutch that drives automotive airconditioning compressors.