It's my understanding that the only part of the Ilfochrome chemistry that's in any way different from standard B&W paper chemistry is a bleaching step that either rehalogenates the silver image so it will fix away, or directly dissolves it. The color image is formed by destruction of dyes (already present in the emulsion), and do not depend on dye agents in a developer step as is the case with C-41, RA-4, and E-6 chemistries.

I don't know whether the bleach is similar to those used in B&W reversal or C-41/RA-4/E-6 processes, or whether it has a component that contributes to or performs the dye destruction -- but it should be possible to find out. If the Ilfochrome paper and transparency materials are still available, the chemistry kits may be simply a convenenience...