Yes, you can download files for offline use.
Files that save to Local Files and iCloud Drive are automatically saved offline. Other cloud storage locations have the Download for Offline Access feature.
To use it, select a file from a cloud storage service by tapping the circle next to the name or icon, then tap the ellipsis (...) at the bottom of the screen. You should see a button that says Download for Offline Access. Use this to be able to open the file when you're offline. Once you are connected to the internet the file will automatically sync. But, you can always manually save your work when you connect again as well.
