Some doubting here
I believe that Ron Mowrey (sp?); he goes by Photo Engineer on this site has mentioned, either here , or on other sites, that the dye couplers in the C-41 developer CD4 are tailored for negative dye stability, and that dye coupler in the E-6 colour developer and RA-4 developer, CD-3 are tailored for stability with their respective media.
We know that colour dyes will form when cross processing, but he has has misgivings about them being archival. There was also past commentary on the issues of difficulty of proper fixing of e-6, and the concern that a formaldehyde based final stabilization bath may be important for archival issues, even if it is not common due to current environmental issues.
On my own front, I have mis-misgivings about calling anything not straight black and white silver as archival. We know that even properly processed dyes fade. Well maybe not all - I think of Kodachrome off the top of my head as being very stable.
But I think that cross processing, while intriguing, and neat to 'play' with, is a long way from calling itself archival.