Wouldn't it be much more useful to store ALL project related stuff inside project's download directory instead?
However Offline Explorer cleans them up automatically after 24 hours itself on every launch.
" I thought it was for OEs own special system files. I noticed that the default folder at %AppData% also includes some other files like IBB, IBX and what not - files containing URL info about my last project. Can I safely erase the whole folder instead without harming OE's functionality?"
Erasing the folder would remove all projects that you have now. And the information about downloaded files.