Would a 12V geared DC motor (about 140rpm) (with an encoder) PID controlled as a servo give a study response when subjected to a load?
I'm assuming you mean 12V geared DC motor.
It can give a stable response. In fact, this is done all the time. Plus, if the load is relatively stable, and the gears and other transmission elements have enough friction, you may not even need to use PID - a simple proportional controller might be good enough.
But your question is not sufficient for providing a specific answer to a particular design option, because you can also implement a PID controller for a 12V geared motor under load and have it not work. It just depends on the specifications of motor, the gears, the power supply, the controller (amp), the software, and the load.