Interesting question. Non-reciprocal behavior can be observed in cases where the media has gyrotropic/anisotropic properties. In principle, the transducer is also a part of the media, so even if your media is a vacuum (besides the transducer itself), reciprocity is not guaranteed, especially when the transducer is polarized. I'm not familiar enough with piezo physics to give a solid answer though.
However it has been reported that many media (including many human tissues) exhibit anisotropic properties to acoustic waves.