Yes, iAnnotate 4 does offer offline support. 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, 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. You can always save your work back when you connect again and, once online, your changes will automatically sync.