No, this is a bit tricky to explain though.
As long as you are moving around and aren't being illuminated by another light, you won't be warped into the photo. Long exposure photos keep the shutter of the camera open, allowing any source of light to be painted into the sensor; that light from the sensor is painted onto the photo that you are taking. When long exposures are used in sufficient lighting conditions, the moving objects can be seen as well, although they appear blurry.