Guitarists (or mixers) record IRs by playing a sine wave through their cab and recording that. The difference from the dry vs recorded sample is then your IR. While exhaust systems have no digital input, if you have good enough audio gear that can output the signal dry as possible through the exhaust setup, it should achieve the same result I guess. Not that trivial for everyone to do, but if you do this enough times for different kind of exhausts, you'll also have great dataset to start researching and developing a software that can model exhausts accurately.

You can model it as a series of tubes of different diameters.

Look up "digital waveguide" for some more details. This technique is mostly used in speech synthesis, where it can make pretty realistic human-speech-like sounds by modelling the vocal tract, but there's no reason it can't be applied to a car exhaust system.