Just pulled my camera out of my gear bag (where it has been off for a few days), took the lens off and set it on a table in a sun beam so I could watch the dust falling in front of the lens mount.
Camera, while off, demonstrated a minimal field effect on the dust. (Common household dust, charge unknown)
Upon powering on the camera it then demonstrated a slightly stronger field effect, enough to deflect multiple particles from their downward path such that they landed inside the mounting flange.
So, while the sensor may be covered at this point it has encouraged several more pieces of dust to enter the body. Given that they are no in the body they have the potential of migrating toward the sensor during its normal operation.
Also noted, the field effect has not quickly dissipated after powering the camera off, suggesting whatever charge is causing it will remain for some time after switching the camera to the off position.
However, it should be noted that the total effect of this is likely to be negated completely by simply moving the camera gear around during normal lens changing functions... While the statement may technically be true, in practice it is likely to have such a minimal effect as to be undetectable in real world practices.
Canon EOS 7D | EF 28 f/1.8 | EF 85 f/1.8 | EF 70-200 f/4L | EF-S 17-55 | Sigma 150-500