Lets say the Kinect is sitting at (0,0,0) and facing the +Z direction. Suppose there is an object at (1, 1, 1) and one of the pixel in the depth image from Kinect is representing this object.
Is the depth value reported by the Kinect the distance to the origin (square root of 3) or is it the distance to the XY-plane (simply 1)?
The depth value represents the distance to the XY-plane. I don't know if this is stated explicitly in the documentation, but you can test it yourself:
Just point your Kinect at a planar surface, parallel to the Kinect's XY-plane. All the points on your planar surface should have roughly the same depth value.