From what I know, it's impossible to copy any voice from keyboard to USB or PC. Example, if you "copy" a voice from S970 (or S670) to USB, you only actually copy (midi) settings of that particular voice -such file usually has size of about 1kbyte and does NOT contain actual wav audio data. If you "import" such voice file to another keyboard which doesn't already contain that exact voice, then keyboard will try to find "the best match" of that voice and apply settings from voice (midi) file.
Because of above, that's the reason why one can't "import" voice file into Yamaha Expansion Manager -one can only create new voice inside YEM (if audio wav file is provided).
That is, one can only load new voice into keyboard if a voice exist inside ppf/ppi file. In case of S670, you can use a S970 package and import that into S670.
Obviously above also applies for style voices: if style uses a voice (again, style doesn't contain actual voice -only voice settings) which isn't already inside keyboard, then keyboard will try to find "best match". In case keyboard can't decide about substitute, then there will be no sound for that particular voice.