If you used the Thiele-Small model, then it simulates only the characteristic impedance of a speaker. It does not even try to simulate frequency response, which is a result of vast amount of complex parameters.
I've seen some cabinet design softwares that do model the frequency response of the lower end based on Thiele-Small parameters. I have been studying how to do it once in a while but that theory is strikingly difficult to learn - especially since I suck in math. Anyway, that response can be calculated rather correctly and this is likely the best application for Thiele-Small models.
However, a difficult task would be to model the higher end where the cone movement reaches its physical limit and starts to introduce distortion that extends the bandwidth (break up modes). As far as I know, no one has presented an universal theory (similar to Thiele-Small) of how this behaviour should be measured and modeled.
Then we also have the effect of deliberately limiting the maximum cone excursion, which adds a compressive effect. As far as I understand, this effect was quite pronounced in Vintage speakers and therefore created a false belief that AlNiCo magnets (that were used back then) compress the sound. Thiele-Small model does not provide a means to simulate this behaviour either.
Anyway, most speaker simulators do not try to model specific speakers they just:
- Introduce a steep high frequency roll off @ about 3 - 5 kHz
- Introduce some middle range notch
I can give some examples.
Here is a Marshall speaker simulator, which is sort of medium complexity:
http://www.diystompboxes.com/pedals/schems/msim.jpgA "Condor Cab Sim" from runoffgroove.com is pretty similar
http://www.runoffgroove.com/condor.htmlAnyway, those are not very accurate in modelling all the nuances so it is hard to justify the large amount of components. The best circuit in this respect I've seen so far is Gallien-Krueger's VCV (Vintage Cabinet Voicing), which does nearly the same thing as the above ones but uses only one opamp stage.
If you want to get meticulous these circuits get really sick, though. For example, take a look at:
http://home3.netcarrier.com/~lxh2/marsh.html