yes you can go from an 8k or 12k stone to a coticule.. its possible that the 12k will provide a keener edge then the coticule, and that while imparting smoothness you loose some keenness..
it is probably sufficient to go from 8k to coticule, impart some smoothness, and hopefully bump the keenness up.
in the end you should arrive at pretty-much or exactly the same thing, a coticule edge.
i think part of what you want to know is can you use the coticule without slurry after synthetics. the answer is yes, and different coticules will behave a little differently in how they finish on water. i hope jarrod would be able to pick out a good one for that purpose.