not trying to make you wrong here, but i think your confusing power compression and inductance. First of all, loading a driver in the box is not going to change the TSP's of the driver itself unless you measure them wrong. I have measured woofers in small boxes, and if done right, they produce nearly the same TSP's as free air. you have to calculate the box volume very carefully. There is a larger degree of uncertainty too and minor changes in box volume lead to major differences in the meausrements. its really hard to get right.
if you just measure an impedance plot in a box vs free air, the are going to be totally different and the program will assume its a woofer in free air so the TSP's are going to be wrong unless you tell it its a sealed box of specific volume.
here are some good resources about measurements
http://www.libinst.com/technical.htm
if you're really interested in inductance, i recommend you read this paper.
http://www.cedrat.com/applications/software/doc/voice_coil_Celestion_loudspeaker.pdf
in short, i'll give it to you. the iron makes for a very good inductor core because it has high magnetic permeability. put current around an iron core, and you have an inductor that can store and then provide large amounts of magnetic energy.
iron is in steel, but steel is also partly conductive. Steel is one of the primary materials in a motor and acts as a lossy inductor as well a shorting system (like a shorting ring)
a voice coil is AC, so its going to charge and discharge the inductor (motor) each stroke, but it also has a moving magnetic field which moves thu the steel. Steel is used to complete the magnetic circuit of the fixed magnet, but it can also be interfered with from the moving magnetic field of the voice coil. If the steel is not 100% saturated, then the voice coils magnetic field is going to modulate the magnetic flux inside the steel. - flux modulation is basically the phenomena of steel being used as a DC magnetic return path as well as inadvertently used as an AC non-linear inductor, but like i said, steel is also like a shorting ring near the surface where eddy currents travel so it partly helps itself. But this has nothin to do with the box, its simply the voice coil and the motor interacting.
audible transient response is really silly because its really a matter of the delivery of sound rather than the distortion. we're talkin time domain stuff here
if you want to learn about the psychology of distortion pertaining to the time domain, Earl Geddes has done incredible work
http://www.gedlee.com/
in summery:
inductance is not transient response in terms of what we measure or hear in the time domain.
inductance does have a transient response in terms of how it interacts as a function of current thu the voice coil, but it does not affect the impulse response in the time domain, it reduces sensitivity by increasing impedance as a function of frequency.
they are TWO totally different things.
transient response is a generic word for a state change, so i think people get confused into thinking it only means one thing.