That depends on the conductivity of whatever paths are available to disperse the charge.

Generally speaking, to get very much of a static charge means the object is either a fairly good insulator or that there is an active source of charge. A camera sensor has an active source, so it doesn't generally act as a good insulator, and discharges fairly quickly. There is still a problem though... where does it discharge to and what is the total effect?

The camera is just large enough that spreading that small a charge over the entire camera is enough to make the sensor area less of a dust magnet.

Note that by "fairly quickly" in terms of a discharge, maybe from half a second to 2 seconds. Faster discharge times, due to a highly conductive path, might result in a variety of effects from ESD (Electro Static Discharge) such as induction of a charge into nearby conductors.