If the client continues running, it will operate with the last network map it received even if unable to reach the control server. Currently active connections will continue working. If the client has not tried to reach a particular device on the same LAN recently, it may not know that device’s LAN address due to some battery life optimizations that were made on the control server a little while ago – that information is now typically distributed on-demand via DERP, so if you don’t have connectivity to the DERP relays then it won’t work. If the client restarts, it will not remember any of the details about other devices on the tailnet.
In conclusion, there are some circumstances where this would work fine but it will be a fairly brittle setup and there are situations where it will fail. I can’t give you a strong recommendation – it’s going to depend on your risk tolerance and ability to work around issues when it occasionally doesn’t work out.