About
TeamViewer: yes, apparently it could be possible to run it locally only. Since the article says «Note: If you choose Accept exclusively, TeamViewer will disconnect from the internet – that means it will no longer be possible to make or receive connections using the TeamViewer ID [...]», and given that the local addresses cannot be reached by the online TV servers, then the two local TV "client" and "server" should be autonomous. Good find.
The article:
TV Knowledge-Base - Can-TeamViewer-be-used-within-a-local-network-LAN-only