Well, I've never tried this particularly, but the
PortableApps.com edition of calibre uses the standard PAF launcher which (among other things) fixes filepaths when the drive letter changes.
Presumably, it will fix this one too, if not then that is a bug in their launcher code and they'll fix it.
As for the "official" calibre portable, it doesn't really mess with the configuration at all (it merely uses the config relocation environment variables, and passes the --with-library switch) so you are probably out of luck with it.