Can a 20-second exposure in bright light damage a camera sensor?

If you are talking about normal lighting conditions, then overexposing a photo that results in a totally white image will not damage a camera. After all, if there is any pure white in a scene, that spot on the sensor is totally saturated when properly exposed. Such an exposure does not damage the spot on the sensor that records the pure white, does it?

If you are using a mirrorless camera, other than the very brief times when the mechanical shutter closes/opens to expose the image/closes/reopens to continue Live View, the imaging sensor is exposed to light for the entire time the camera is turned on. Under very bright daylight conditions the camera is not damaged even after many minutes of continuous use. The same is true with shooting video. Even in very bright conditions the sensor is not damaged when exposed to light for several minutes or even hours.

Where you will get into problems is if an extremely bright direct light source, such as the sun or a powerful laser, is inside the camera's field of view. In that case it might not even take a long exposure to damage the camera. Lasers with enough power can damage a sensor almost instantly.

Damage from pointing the camera at the sun is usually heat related and takes a bit longer. Longer focal length lenses, which concentrate more of the sun's energy, can contribute to major damage:

With wider angle lenses and a camera with a mechanical shutter that covers the sensor at all times except when the image is actually exposed, it is possible to take images that contain the sun in the field of view without damaging the camera. Be very careful not to look directly at the sun in the viewfinder, though, as the sun can damage your eyes!