Originally posted by ffking so the AF sensor has a more certain signal to work on and can therefore make its calculations quicker, thus quicker AF.
My understanding of AF sensors is that they only "see" a small strip of light and a basic histogram is compared to the other sensor strip at that AF point. Regardless, the AF sensors themselves don't do any calculations, the signals they produce are combined by a processor in the camera to estimate how long and in which direction the lens' AF motor should be operated. AF sensors produce continuously varying signals, which are read at points in time by the camera processors. There is no lag in the sensor, any delays in calculating instructions for the AF motor are produced by the camera's processors.
Phase detection AF in DSLRs doesn't involve the camera's image sensor, so moving the image sensor to stabilize the image (IBIS) has nothing whatsoever to do with AF. Moving the lens elements to stabilize the image (OIS) will affect the image detected by the AF sensor strips, but unless camera shake is affecting the lens motor instructions calculated by the camera, using optical stabilization doesn't aid or hinder AF either. Unless the AF system is precise enough to detect when the lens changes from being in focus to out of focus because of camera shake, OIS should have no impact on auto focus. The key in this is that image stabilization reduces changes to the image from camera shake while the image is being recorded, it doesn't bring the image into better focus. It is possible to take a blurry picture that is in perfect focus.
Contrast detection AF is a different beast and depending on how much of the sensor is compared each time, there could be situations where the camera gets confused by camera shake as to when the focus point is actually out of focus and when it is in a different position. In practice I doubt if this is an issue and even if it is relevant, it wouldn't matter if the image is stabilized in the lens or in the body, the degree of stabilization obtained would be the determining factor.