In my experience even a "saturated" sensor (with light bright enough to cause all pixels to read full-white, but not bright enough to cause damage) will still generate some random noise, although far less of it.
(Ironically, the cheaper the camera the more noise it is likely to have, and thus be better for this application...)
(Ironically, the cheaper the camera the more noise it is likely to have, and thus be better for this application...)