Yes, this can be done. The DVD player only cares about the VIDEO_TS and AUDIO_TS directories. You can create additional directories and store whatever you want in them. You can probably even put some autostart files in the top level directory without bothering most DVD players.

However, you won't be able to make this sort of disc with MyDVD. You'll have to use some sort of DVD authoring software that lets you produce the DVD image in a folder on the hard drive first, then use some sort of disc burning software (Nero works well for this) to write the DVD with the additional directories.