I don't expect that having the camera off will stop the static fusing dust onto the sensor.

I'm not an expert but what makes sense is:

Sensor is only statically charged/charging for the duration of the exposure.. otherwise the sensor is always turned off(even tho the camera is in the On position)

the sensor only needs to be electrically active for the duration of the exposure.

of course Live View changes that, and you'd expect that if you use LiveView more often than not then expect to have more dustbunnies. Of the cameras that I know of, there are none that have LiveView as an option, that don't also have sensor cleaning.

I remember reading of a chap that made a static dust gun, where he used a static charge type fire igniter and disabled it's ability to cause a spark. He used to aim it at the sensor of his DSLR and give it a couple of shots, and the resultant static charge(but no spark) loosened the dust prior to him either using a blower bulb or canned air to blow it out. Worked well from memory(but that was 4 odd years ago, and I've since lost the link to his homebrew contraption).