If the rod was never pulled, would you be able to breath the cylinder to near empty, albeit with increased resistance, or would it quit delivering gas until you pulled the rod. I never tried this myself, so do not know the answer. I always pulled the rod when the resistance increased and did my ascent. If the latter is true, then it does, indeed, make more gas available.
Now my understanding is that when the pressure of the cylinder reaches a low pressure, it then engages the spring, so it does take an action (restricting air flow) when a condition occurs (low pressure). Pulling the lever disengages the spring and you can resume breathing as effortlessly as previously.