From a microphone perspective, this is a trivial problem. If you can afford one (or borrow one from a university lab), you use a NIST-traceable measurement microphone (or whatever the EU equivalent of that is). If you can't, you obtain a second-generation calibration, or failing that, any of the uncalibrated measurement microphones on the market. The frequency response of all such microphones will be essentially flat from 80Hz to about 10kHz, which is about all you can reasonably analyze anyway. Distortion at the sound pressure level generated by an
acoustic guitar at 1 foot or so will be well under 1.0% THD, likely less than 0.2%, and will be mostly second-order. Given that guitars have a first harmonic that is many orders of magnitude larger than that, such distortion will be far less than your likely measurement resolution.
That was the easy part. From a guitar perspective, it's rather an interesting question; probably a good one for muttley as that is his specialty. The observed timbre (that is, the relative strength of various overtones) I imagine will vary by mic position. It also varies quite a lot according to how the instrument is played--primarily where it is plucked, and how, etc. So I don't think a objective response for "accuracy" can be stated. The variation in response can be easily measured, however. You can try to control for performance, or you can just create a large sample of notes and average them. Best of all would be to have a bunch of mics so you are analyzing the same performance, but that could get expensive.
A possible methodology would be to measure harmonic content at three positions close-miced (1 foot; lower bout, soundhole, 12th fret), and then at 3 feet aimed at neck/body joint. An anechoic chamber is not really required for this sort of analysis because the contribution of room reflections to measured amplitude of each harmonic is small. But use the largest room you can find anyway.
I would measure single notes across the full range of the guitar (say, play up fifths from bottom to top), allowing each note to decay to -60dB from peak, then create a waterfall graph of the resulting decay. Ideally, you would be able to restate each graph as a function of the overtone series rather than just frequency. Hint: use a pitch-shifting algorithm to normalize all pitches.
Next, you have to create a mean response for each mic position. Note that you will see the largest variation perhaps when you shift from wound to unwound strings. You can ignore that and average them anyway, or treat them separately. An easy way to generate the mean response is to mix all of the observations from each mic position, then you would end up with five waterfall graphs which you could then quantify the difference in overtone response.
I would finally point out that there are software programs such as Wavelab that have all of the tools required to perform this analysis without having to sort through a plethora of VSTs . . .
The great question is whether that will reveal anything different than a simple measurement of variation in frequency response; I don't know the answer to that offhand. I suspect it does; otherwise a recording engineer could simply use a single mic position and use EQ to compensate.