Can I listen to iTunes audiobooks on my 4GB iPod?

Yes, you can. Just make sure it is not set to shuffle.🙂 iPod shuffle: Playing audiobooks and podcasts - Apple Support

-AJ

Is this a 4th gen iPod shuffle (not "4GB iPod"). If so, audiobooks are treated as playlists. First, sync the audiobook to the shuffle, either manually (drag and drop on shuffle in iTunes) or by setting up the iPod's Audiobooks settings screen in iTunes.

When playing the shuffle, use VoiceOver to select the audiobook from the playlist menu. The power switch setting to shuffle or play-in-order does not matter, when selecting audiobook from playlist menu. This document explains how to set up and use VoiceOver.

iPod shuffle (4th generation): Enabling and using VoiceOver - Apple Support