I've never observed any correlation between high efficiency speaker and improved performance at low levels. Rather, (again, IME) the most important characteristics to enjoyable listening at low volumes are resolution of low level detail and microdynamic shading (as opposed to macrodynamics). These can be found, to varying degrees, in both higher and lower efficiency speakers.
With that said, at the extreme, I have noted as a characteristic that very low efficiency speakers (e.g., <84 db/W/m) tend not to be very good at preserving microdynamics.