The Kodachrome process was very complicated, the film consisted of many layers. The color development portion of the process consisted of three separate color development steps. The film did not contain any color couplers. Each of the three couplers was in a separate color developer. It is incorrect to think of the Kodachrome process as a black and white process. There are several sites on the web that explain the process.
While it is theoretically possible to retain color information using only BW developers, most of the Kodachrome process would still have to be used. The film would have to be re-exposed three times and developed three times. This is something that is no longer possible since the last machine that could do this is now gone. Not only that but there seems no way to obtain the color information from such a BW positive without being able to scan each of the three layers containing a BW positive seperately. No scanner at present can do this. You would need a cross between a scanner and a microscope.
The coup de grace is that no one is making this film anymore. The coating machines for it are long gone.