AppImages are "portable" in the sense that you can copy the one app = one file to a different system and it should run.
They are not portable in the sense that data (such as created documents and/or settings, caches) travels with them.
But on Linux, this is quite easy to achieve:
Simply launch it like this:
export HOME=/where/you/want/your/data ./some.AppImage. You can even put something like this into a script.
If have been considering to make the following feature: If there is a directory with the same name as the AppDir and a special suffix present next to the AppImage location, then use that as the $HOME for the AppImage. Would you be interested in such a functionality?