I discovered that some audiophiles can't identify whether system has inverted phase configuration or not. I wonder if there's anyone holding DBT event about phase inversion before. I tried searching in Google found no result.
That's correct. I'm talking about inverted phase of both channels which can happen from a few circumstances like different Hot/Cold XLR, some RCAs using inverted signal as output, swapped speakers cables, etc. It'd be interesting to see DBT of such events and see if most audiophiles can detect that.
What you're actually referring to is the concept of "absolute polarity". The ability to detect a difference in signal polarity is determined by the degree of asymmetry in the signal. For most musical signals the waveform is fairly symmetrical about the zero baseline. However, certain voices are highly asymmetrical, and when polarity is reversed they do sound very different. The trouble would be determining which is correct. The idea of positive air pressure producing positive voltage throughout the system and positive air pressure from the speaker is a nice thought, but in reality, polarity is random. There are many chances for inversion along the production path. And while asymmetrical voices do sound different when polarity is inverted, it is not possible to determine which is "correct". The problem becomes one of OCD.
This issue comes up in AM radio broadcasting where modulation limits are also asymmetrical, with 100% negative being the max permitted (and distortion results beyond that quickly), but 125% positive is permissible in the USA. Broadcast processors have used some form of phase/polarity optimization for many, many decades to ensure their their highest peaks are always positive.
There are three basic techniques. One is to detect asymmetry and hard-switch its polarity for maximum positive, and it turns out, that switch action is very audible on asymmetrical male voices (confirming the polarity audibility argument), though effective. The second much more graceful technique is to use the output of a polarity detector to sweep the cutoff frequency of a single stage 180 degree all-pass filter through the passband. This is essentially a soft polarity flipper, and is nearly inaudible in it's action. The third is to use a fixed all-pass phase shift network to "scramble" phase over the entire spectrum, which removes the asymmetry completely, eliminating the issue. That, too, has an audible effect if you were to switch it in and out, but once in place, its presence is quickly accommodated, and it isn't noticed....much. It's a very old technique, and there was a product marketed over 40 years ago that did it completely passively called the Kahn Symetra-Peak. So far, the second method is the best, and still used in AM processors today.
So, yes, polarity is audible given the right asymmetrical signal, of which certain male voices is the most common. Not all voices, male or female, are highly asymmetrical, though. Strings and woodwinds are very symmetrical, some brass no as much, but music, in general, is pretty symmetrical in nature. Percussion is asymmetrical, but also very transient and thus more difficult to differentiate polarity with.
When a signal is symmetrical, inverting polarity doesn't change the aural stimulus at all, so it's not heard. There are degrees of asymmetry, and thus degrees of polarity audibility.
Doing an ABX test to confirm polarity audibility would really be a test of how audible a polarity inversion is on a specific signal, not audibility of inversion in general. It wouldn't take an audiophile, when it's audible, anyone can hear it.