Thinking about this some more (you guys know I like to think about this stuff) I think that the IR of a microphone might not be that useful actually.
IR and Frequency Response are conjugate properties: they are related to each other by Fourier transform. So, talking about IR is equivalent to talking about how the system described by the IR filters the sound.
Microphones are indeed filters, however they are "pretty hard to deal with filters". I think that most modern microphones have a reasonably flat frequency response when they capture on axis free field sound only (that is, a plane wave sound emitted by an infinitely far away source that is impinging right in front of the mic membrane, in a open infinite space without reflections whatsoever) [*]. This sort of response would be, if we want, the nominal response of the microphones, what we see reported in frequency response plots like
this one [*].
As a result, I think that for the most part what makes microphones different from one another is not really the frequency response. Most modern mics have perhaps similar unexciting flat or flattish response (a part perhaps for some resonances).
Probably what makes the real difference is actually directivity, that is, how the frequency response changes by changing the relative source and mic orientation. This alters dramatically the sound as captured in real environments (in which there are reflections, impinging on the mic from many different directions), from real sources that, moreover, have a directivity of their own too. I don't really see any way to model or measure easily directivity of different microphones. Also, there aren't ways to apply it to recorded sound, as the information on the original position and environment is lost. Undo directivity from a recording is substantially impossible for pretty much the same reasons.
So, recording the "nominal" IR of a mic in certain conditions is possible, as well as it is possible to model it. However, it is still not telling the whole story. And I think it might actually be telling not even the most interesting and relevant part of the story.
If the target mic is also nonlinear to an appreciable extent things get even more complicated: IRs do not work well for nonlinear systems.
As a result I would say: perhaps best to have few reasonably good mics and use them wisely. No need to try to emulate expensive ones: they are not the best solution in every case anyway [*]. No simulation/emulation can undo wrongs done while recording (bad mic placement, for example).
[*] This sort of sound can be reproduced, within a frequency range, only in anechoic chambers, by using speaker arrays.
[*] It sounds awfully complicate to measure mics responses then, but actually there are known methods to make it much simpler without sacrificing accuracy significantly.
[*} It would be nice to see a rigorous double blind listening comparison of many different mics. I suspect that the correlation price VS subjective rating might end up being not too significant. It would be a quite hard experiment to set up, though.