The old Kodachrome processes were designed for Kodachrome films with the old style hardeners, and therefore were run at low temperature or had a prehardener step with neutralizer much like E3/E4 did. The oldest process was more like E1. The current process is more like E6 in temperature and process cycle but as you note all Kodachrome processes use 3 color developers. I have posted the current process cycle for Kodachrome elsewhere.
It is possible to develop any Kodachrome film at home by hand given the formulas and couplers, it is just labor intensive and exacting. It was regularly processed by hand in the Kodak research labs, as there was no other way to process the small amounts of experimental coating we sometimes made up. When the process was the varaible in the experiment, it was often necessary to work with 1 liter or less of a particular processing solution if a chemical was only available in limited supply.
With determination, it would be possible to process any variant of Kodachrome or any other color film today to give a color image. I would question the results though due to keeping. Color films, on average, keep less well than B&W films, especially the older varieties before about 1970. This is not necessarily true of Kodachrome, as the extra coupling chemistry is not present in it and this has been one of the problem areas, but some variants of Kodachrome have been known to keep poorly for a variety of reasons.