neither bringing the cue away from the background, or using a neutral background will make the camera better focus on the subject.
even with auto-focus, the photographer has to take care of focus.
you can use spot focus to make sure the cue is in focus.
then you can shorten or lengthen the depth of field (dof / area in focus - front to back) as needed, with the aperture setting.
the smaller the aperture (higher number), the wider the dof, but requires increasing light.
when it comes to taking pictures ,you can spot me the 4 ball! i use a cannoneos40d with a 17-85 lense and use auto focous and hold the cue and camera . but my pics will never be as stunning as yours jeff happy new year!