Not sure which version of Anim8or you're using but if you're using the latest development release...
If you have just a '.' in File->Configure for the texture directory, then it checks the original absolute directory, and it searches the directory that the .an8 file is located in and its subdirectories. If you have a texture directory specified in File->Configure, then it'll only do the search in that specified directory and it'll search in the root directory that the .an8 file is located in (no subdirectories). So if you want to be absolutely safe when transporting/packaging your files, you can keep all the textures in the same directory as the .an8 file (not in any subdirectories), and it'll load it even if the user specified a texture directory in their configuration.