I should think it could be tested - it's very similar to the comb filter experiment mentioned in Amir's paper earlier on..?
Another way of looking at it might be simultaneous equations. There's only one unique acoustic solution that would explain the result we hear, particularly as we move our ears around in 3D space.
If we really do hear through the acoustics, then for it to sound neutral to us the speaker would have to be neutral in terms of frequency response
and phase/timing i.e. reproduce the signal verbatim. As Mr. Watkinson
claims, when we fail to preserve the phase information using, say, a conventional crossover filter, we still recognise the results, but they have lost their absolute realism.