All modifications to a document on one device will immediately be available on a secondary device without requiring an internet connection if both devices are configured with a cloud-based file synchronization service.
For file synchronization to occur between devices using a cloud-based service, an internet connection is necessary. Synchronization without an internet connection would not be possible as the service relies on a network to communicate changes and update files across devices. Hence, the modification would not be immediately available on another device until internet connectivity is restored and the service can synchronize the files.