I seem to remember that the path of philosophy does run from Ginkakuji to Nanzenji. At least, we spent a day that included the Nanzenji and Ginkakuji and we walked the philosopher's path between them, so it probably does but I'm not sure if it is 100% of the distance.
Its a really nice walk anyway. I think you can squeeze in most of the sites between Ginkakuji and Kiyomizu dera in one day, but it'll be a busy day. Probably it would be best to start at one and just walk to the other and decide as you go which spots are of most interest to you as you pass them.