Yes, that’s what sync does. But it would be possible to connect these two local vaults to the same remote vault, right? This would essentially accomplish what you want (I think).
With Sync, the common notes in the Venn Diagram would be stored in the Obsidian server and synced down to both local vaults.
This shouldn’t be a problem with Sync either as far as I know.
I can’t speak for that “external directory” outside of the vaults you want to use (it might be hard to let Obsidian know that it must watch a folder that is not a vault) nor the nested vaults (which I don’t personally use).