I'm not sure how easy to detect it would be. I might be wrong here, but tend to think of it this way - you can alter the phase just by moving your head. In doing so, you alter the time at which the signals reach your ears. That's much more easily done at higher frequencies because of their shorter wavelength. A quick Google suggests that at 50Hz, the wavelength is just under 7m, so it's hard to have any real effect on phase by moving your head, and hence why incorrect phase is easily detected with bass. . But at 15KHz, the wavelength is less than an inch. So moving your head half an inch further from one and half an inch closer to the other would make them out of phase - but moving your head small distances doesn't have that effect.
So, does the brain just compensate, as it would have to in the real world?
Or am I barking up the wrong tree? Wouldn't be the first time...