Well, if you know the inductance of the PUs (ideally, also their AC ESR due to eddy losses), the resistance of the potis and capacitance of the cable (and of any tone caps), you can quite reliably predict the total response as the linear filter resulting from these components, and that's not too hard to grasp using complex analysis – just apply Kirchhoff's laws with Ohm's to all the AC complex impedances. That response can then be simulated with any standard digital IIR equaliser using biquad filters. To estimate what difference a given change to the circuit would make, simulate both the original and modified circuits this way, but invert the response of the original.
So far, it's somewhat obvious.
What's not included in such a model is the influence of the positions of the PU(s), of phase effects between them and so on, and that's perhaps the most interesting aspect. In principle, this is also easy to model with comb filters (there's also some nonlinearity in the string-pickup interaction but that isn't really affected by the circuitry).
Unfortunately, these effects influence every string in a different manner, so it's not really possible to simulate the changes from just the mixed guitar output. It is only really possible with signals from a hexaphonic pickup.
These calculations are of course exactly what processors like the Roland VG series (now merged with the GR series) do, as well as modelling guitars like the Line6 Variax models (though these, judging by the bad transient response, appear to actually use a FIR/convolution approach rather than physical modelling). Problem is, AFAIK none of these allow actually customising the simulated circuitry.