Depends. If shooting with one shot focus, the focus is locked when the BBF is depressed (not necessarily locked on the subject, but just locked at the focusing distance). Therefore, when shooting wide open and with such a shallow DOF, especially with a f/1.2 lens, recomposing may change the distance to the object and render your intended subject out of focus. The best thing to do is to select a focusing point and lock focus on the focus point without recomposing your image. Use live view if needed.
If on AI Servo, then the subject would be tracked if you are using all your focusing points. Otherwise, if the subject is no longer on the focusing point, then the AF system cannot track the subject.