In fact, I would bet you could easily hear the resonances if pressed to do so. I find typically, people just never notice them because they assume it is part of 'speaker sound'. However, when I have presented people with opportunities to compare a non-resonant reference to the standard resonant one, the resonance seems to become obvious. There seems to be no special hearing required; simply an opportunity to be exposed to a pure reference. However, once used to resonant free system, one seems to more easily recognize resonance when it is present. Personally, I can not stand most speakers, partially because of this issue. Sadly, most speakers (even so-called high end) seem to be horribly resonant. Floyd Toole did extensive research on resonance audibility, and it is no small issue to brush aside if high fidelity is truly desired. Based on the cabinet schematics you posted here, I would expect a high degree of timbre distortion to be present, due purely to the cabinet panel resonances. To produce a cabinet with low acoustic output requires an extreme solution.
-Chris