[eigenket]

I'm a physicist but not an expert in this field, but my guess would be the answer a comprehensive "no".

The way satellites orbit is incredibly well described by Newtonian mechanics and there the impact of their mass on the shape/timing of the orbit is by changing the center of mass of the combined satellite-earth system. That is you only get measurable effects if the fluctuation in the mass are big enough compared to the mass of the earth.