Yes you are understanding correctly.
I put together a small test to try and highlight it further by putting the same event you have into Pawns on a listenserver (One client acts as server)
You can see the first output is from a Pawn I spawned on the level blueprint to simulate an AIControlled Pawn:
Server: Is NOT Locally Controlled AND Has Authority
This makes sense as the Server is controlling it so it has a [Network Controller][2]
The rest is as you have understood. The blue logs are when the Pawn becomes unpossessed and the purple logs are when they have a PlayerController possessing them.
Let me know if you have questions or concerns and maybe I can expand this answer further 