No. Comets masses are too low to detectably perturb anything normally, thus the only way to directly measure the mass and calculate the density (beyond simply establishing upper limits) is by monitoring the trajectories of passing spacecraft or by monitoring the amount the comet itself is perturbed by its own outgassing. The heavier the comet, the less it will be perturbed. Estimations of Halley's mass using this latter method yielded a density of about 0.7 gm/cm^3. This method is not as accurate because you need to know the velocity of the outgassing as well as extremely exact positional information for the comet over a period of time. Atmospheric seeing limits spatial resolution of most deep space images to an arcsecond or more, thus the "resolution" of measurements made this way is limited as the amount of perturbing due to outgassing is very small over the short time spans associated with the close approach of a comet.