Yes, spinning the motor shaft will generate voltage.
On a standard, cheap DC motor you will feel cogging but an actual PMDC servo motor has very little cogging and is smooth and easy to spin by hand.
The output stage of the servo drive is, most of the time, an H-bridge built with MOSFETs. These MOSFETs contains diodes which basicallly forms a bridge rectifier with the motor at its AC terminals and the servo drives power supply at the DC terminal.
This bascially means that the voltage generated by the motor gets rectified and placed across the drives power supply. If you spin the motor fast enough it's possible that voltage generated is high enough to actually power up the drive (if the drives logic supply is derived from the motor supply).
Easiest way is propably to have the drive powered up but with the output stage disabled (if the drive has an enable input). That way the DC terminals on that "bridge rectifies" sits at whatever voltage the power supply delivers and there's likely no way you can spin the motor fast enough to get any current flow. Basically the motor terminals are "open".