Saving and reopening a .blend
Synced objects are ordinary Blender objects. They survive saving, and the file opens normally with no add-on running and no Rhino present.
Each object carries custom properties recording its source, its Rhino id and its detached state. When you reconnect the same document, the add-on scans the scene, re-adopts those objects by id, and updates them in place rather than importing a second copy. Detached objects stay detached.
If a reconnect ever does produce duplicates — most often after renaming a source or toggling Shared source — press Purge stale sources to remove the orphaned set.