It would depend on what the dust consisted of, but offhand, I'd sort of doubt that the sensor would be able to heat up enough (between buffer size limits and frame rates) enough to cause problems with dry particles. Moist particles (salts, for instance) may get warm enough to evaporate leaving a residue, but even organic matter (pollen, say) would need a prolonged exposure to a fairly high heat to adhere.
One thing to bear in mind is that IIRC particles are more susceptible to a charge under dry conditions (think static electricity), so unless you're dealing with hydrous salts, it'll be mostly pretty dry particles being actively attracted to the sensor, and they'd be less vulnerable to heat levels likely in the camera.
A second thing to remember is that what the particles end up on, in active use, isn't the sensor proper, rather it's a clear cover over the sensor. This will further reduce the heat any particles will be exposed to.