Yes, what you're referring to is commonly known as a "loudness" function. The usual way it's implemented requires a special volume pot with an extra tap slightly below the mid-point of the pot's travel. You would connect the tap to a special R-C network so that when you turn the pot towards minimum volume, the midrange frequencies are progressively attenuated more than the bass and treble, simulating the Fletcher-Munson curve.
Problem is, the compensation is not exactly like the Fletcher-Munson curve. It would require a much more sophisticated equalizer to accomplish that. Also, the amount of compensation is based on volume pot position, not actual perceived SPL. Which means it is most likely always the wrong amount of compensation unless you have control over the output level and gain of your source and amp, as well as the efficiency of your headphones, not to mention program recording levels.
Thus, such a scheme is at best just a glorified bass and treble boost control.