How does the output stage react when current is being returned into the amp ?

From what I remember, this is due to the storage of charge (voltage) of a capacitor and magnetic field (current) of an inductor. All behaviors characterized by a set of linear differential equations that result from Maxwell's equations if I remember correctly. Laplace transforms are used to solve the resulting polynomials instead of the differential equations directly. If the excitation is sinusoidal, the phasors can be used. Transients can be found if initial conditions (voltage and currents) are known about the circuit prior to excitation.

Now how exactly, to the mosquito fart detail. I dunno. It probably depends on the amp. Use Spice or something. If the models don't fit, specially the non linear ones that are not covered by Maxwell's and so, I guess refine them.

Do all amps work like a perfect true 0 Ohm 'short' or does it introduce distortions, which ones and how much ?

No. Amps don't necessarily behave the same IMO. Non-linear distortion is likely due to non-linear interactions which are likely poorly described by back EMF and unique to a particular amp and load combination.

Has anyone ever tested for this ?

In many designs (not necessarily here), I believe so.

It may not reveal anything at all as the currents are very small.

Distortion is supposed to be small yet problematic.

In case of the HD600/650/800 the back EMF current around 100Hz is half that of the supplied current around 1kHz so substantial, but still they are very small currents.

You can call the hump around 100Hz on those headphones back EMF. I rather see it as a characteristic of the headphone reactive load.

It is not a textbook test, just an idea to ADD to a test suite and may (or may not) give additional information about the amps performance. Was just a musing anyway, nobody has to (nor probably will) ever build it.

This is IMO not new. I think such model loads have been built in the past for tuning the cross over of speakers. If it strikes our fancy to do it, we'll do it.

Yes, upon second thought, the reactive component of a real headphone load is adequately modeled with the passive equivalent circuit. We can't model the non-linear component but the passive load put forth should still reflect energy back to the amp. The definition of reactance...

Yep. That's how I think things work.