No. The damped thin-walled cabinet design approach is to reduce the audibility of the colourations that the cabinet introduces into the reproduced sound, which are often associated with structural resonances.
In broad terms, the sensitivity of the loudspeaker system depends on the mass of the diaphragm, the strength of the magnet system, the windings in the voice coil, and the stiffness of the suspension. More mass in the cone and voice coil means lower sensitivity. For a given material, more mass in the cone allows for a stiffer cone from increased cone thickness, so that the cone better responds to input signals.