Usually, no. On most point-and-shoot cameras, the lens is covered or the internal shutter closes when the camera is off, so the sensor is not exposed to incoming light.

Even on designs without an external lens cover, there is typically a closed shutter or similar protection when powered down. That means direct sunlight normally will not reach the sensor while the camera is off.

More generally, sensor damage from the sun is mainly a risk when the sensor is active—such as during live view, composing on the LCD, or taking a photo—because intense light focused by the lens can overload or overheat sensor circuitry. Lasers can pose a similar risk.

So for a normal point-and-shoot that is powered off, sunlight is generally not a significant sensor-damage concern. It is still wise not to leave any camera aimed at the sun unnecessarily for long periods, but under normal use an off camera is well protected.