**Note**: Enabling your entire Drive to be available offline is not recommended on a shared Chromebook. Also, keep in mind the Chromebook must have enough storage space to hold the contents of your Drive.
Before you turn on offline access
You can turn on 'offline' editing for Docs from a Chromebook. You can also turn on 'offline' editing for Docs from a Mac or PC. Same account, different device = different settings. Keep in mind the device you are using when you need files offline.
The article "How to use Chromebooks Offline" by Matt Miller mentions adding the "Google Docs Offline Chrome Extension" in order to use offline editing. Google's support page also mentioned this extension. This extension is only required when on a Mac or PC. Chromebooks do not require this extension.