Sure you can hear the circle of fifths if you're lucky or if you know about it and then try to hear it.
But, can the listener hear the performer's level of understanding regarding a musical concept like that, as a part of the performer's being, so to speak ?
Ultimately the basis for our music is the logarithmic overtone scale, and randomly i would claim that this scale is so fundamental that most music in some way revolves around the relationships inherent in this scale.