It should help a bit. There is a technique called "vista buffer" which should be more efficient though, if you already implemented a bounding box tree:
Additionally POV-Ray uses systems known as vista buffers and light buffers to further speed things up. These systems only work when bounding is on and when there are a sufficient number of objects to meet the bounding threshold. The vista buffer is created by projecting the bounding box hierarchy onto the screen and determining the rectangular areas that are covered by each of the elements in the hierarchy. Only those objects whose rectangles enclose a given pixel are tested by the primary viewing ray.
You still need to calculate refracted and reflected rays per pixel though (at least if you have curved surfaces), also the texture and lightness. The intersection checks are suprisingly fast in many cases, compared to texture and light.