Can a helicopter be stable without moving the control inputs?
In answer to your main question, Yes that is how they behave.
In theory in a perfectly world, there would probably be some sort of balance point, but in real life there is always something slightly affecting the helicopter causing it to start to drift.
As for how to actually fly, beyond telling you to get real lessons [don't do it], the strategy of constantly moving the controls is something sometimes called &quot;stirring the pot&quot; and in real life is generally a sign of an inexperienced pilot. With training and experience your control inputs will eventually become so small and so far &quot;ahead&quot; of the aircrafts movements that it will look like your not moving your controls. if you are not using full size controls for your sim, this may be impossible to achieve.