Yes! All Slumber content can be accessed offline.

However, this is only true for content that has already been downloaded onto your device. If an episode is downloaded to your device, the download icon will be green:

You can download all episodes, as well as manage which episodes are stored on the device, by opening the Slumber app, and tapping:

Profile tab > Settings > Manage Storage (on iOS)

Profile tab > Manage Storage (on android)