Digital circuit simulators can basically model the behavior of analog circuits with an accuracy sufficient to make it sound identically. The computation effort won't be acceptable for real-time emulation, however. I presume that usual effect emulators are performing a considerably simplified functional simulation. This means that the emulation isn't a blunt copy of an existing model rather than an intelligent redesign. That's why artistic skill of the instrument/software designer plays a role and results can be quite different.
I also keep my previous comment that many historical analog effects probably never have been exactly modeled yet.