If Tremulous stores your binds/settings, then the folder exists. Maybe it is hidden (check preferences for whatever you are using to browse folders)? Tho yes, you can change the location of homepath to anything, by starting trem with +set fs_homepath "/path/to/somewhere"
at the end of the command/target field of shortcut. It might even be possible to make a portable install of trem, on a USB drive, tho I'm not sure how exactly.