Ok, just tried my Kenko pro 1.4 with my slow 10-20 on an FM, and it seems to work fine. You get the same field of view on FX as you do on DX (eg. with the lens set to 10mm, you get the same field of view with the teleconverter on FX as you do on DX without it), but you lose 1 stop of light, and you are putting more elements in the path, so there is not advantage whatsoever.
As mentioned earlier, the Nikon teleconverters won't allow you to mount. I don't have a digital FX body, and I'm not willing to waste a film frame on this (maybe later) so I don't know how good this actually is. I still think the reason for this is dubious, but it does indeed work, in case someone want to go do this.