It is one of the approaches used, in most cases they use combined approaches, some developers prefer to start from this, simulating the circuit and improve module by module to get closer. (an inductor saturation or a electrol cap with certain bias are things sometimes needs to be measured to get the parameters for the simulation)
Other approach is to grab the thing and look it as a black box and start to introduce different signals and start coping from there, with analytic transfer response approximations. (They are discrete, analytic in the sense it's not convolution or a table f values, but an expression, MACs (multiply and accumulate) are preferred for DSP processors for example)
Acustica audio is doing it in a different way, the convolution we all know for reverbs is one sample of the thing, you introduce one signal and you get one transfer response, in phase, amplitude and time. Nebula is using multiple signals to get the harmonic distortion and dynamics, making it usable up to a really good point to make possible the convolution of non linear systems, while convolution is a approach for linear systems, with multiple convolutions you can get a stepped non linear, then nebula gets in where you can smooth the change between sample and sample if it's generating artifacts and other funny controls. Also nebula have a background of math involved as signal managing, dynamics, filters, which allows to use it without the use of convolutions, or combined which is usually the case, letting you manipulate the signal even further. It does eats you processing power but it's a very powerful tool, I never tested running CUDA but IIRC it's a possibility. First time I saw it a few years back it really got my attention as the first multiple convolution plugin I'd seen, I never see any other yet, maybe there are some with that running in the background but this is very alike a reverb where you get your samples and use it for that purpose, and then tweak a couple more values and let a few parameters visible to control it quickly.
I've seen an article on one of those online magazines about exactly this where they interview people from the major companies doing plugins and they talk about this. That article may be the best answer for your question but I can't remember where it was, it's probably I saw it here first, if I remember or find it I'll let you know.
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