If you have thinnet and they are just peer to peer, if computer B is shutdown, the time that B is shutting down, network connections might get interupted. Afterwards, Computer A should still be able to see C. If computer B is turn on, while B is booting, A & C might get disconnected. If now is accessing at the time it's shutting down or booting up, then your Ok. Now if you have drive mapped between the computers, this might not hold true.
Thin ethernet uses BNC connectors.