Is there a type of servo that can be de-energized and moved manually while giving input back on its position?
What you are wanting to do is to break the feedback-loop in a servo system by removing power from the actuator.  You can do this in any servo by cutting a wire but as the feedback sensor is INSIDE the servo unit you need to add probe wires to read the position back.  

Unless you are implementing the servo function in your own controller, in which case you have the ability to power the actuator off and read the feedback as before.

The case where this is not possible is if the actuator cannot be mechanically driven in reverse.  This situation is possible if there are typical worm reduction stages in the gearing or other techniques used to hold the position in the event of a power failure. A work around here is to manipulate the feedback signal to the control system and have the actuator power to your chosen position and then check or know what the error was that you added to the feedback loop.

In a typical hobby/RC servo the feedback is from a potentiometer and you could read the wiper voltage and compare it to the potentiometer end.  If you have a more elaborate servo system you may have to read out more elaborate absolute or indexed incremental encoders (or other stuff).