Interesting discussion starting here. I would not recommend using the entire image because of possible frame rotation causing errors. The automatic guide star should be a single star selected as close to the image center as possible and with adequate separation from other interferences.
If guiding errors were totally random during an entire exposure, the image would not show star trailing. Instead, blooming of the star would occur. It is because tracking errors are NOT random that guiding works.
Random errors such as winds pushing the telescope during the exposure can not be corrected by this method, but would be caught and corrected by a guider camera.