Not that it cannot be done, but dust will gather on the sensor more quickly, that's all. I believed that you should even wait for a short while so that the sensor can be fully discharge before changing the lens.
Given that the sensor is inactive when changing lenses, as well as sitting behind the shutter AND the mirror, i personally believe the "more dust when camera is on" is just urban myth (aka rubbish). There will be more dust on the sensor simply because dust is introduced into the camera body when one changes lenses, and the dust eventually makes its way to the sensor. The camera being on or off has no significant impact on the sensor dust level.
If there is "static" on the sensor, 1. it would destroy the electronics on the sensor (bye bye camera) and 2. the dust it attracts when changing lenses would be stuck on the shutter.