The way I understand it is that when your work computer drops into the
secure screen it drops your user NVDA settings and loads the secure
screen NVDA settings. So if you have the remote add-on with auto-connect
set for your user NVDA settings and copy this set-up to the secure screen
settings, your work computer will drop its remote connection when the
secure screen appears but immediately re-establish it when the secure
screen NVDA settings are loaded. Similarly, when you log into your work
computer, the remote connection will drop again and reconnect when your
user NVDA settings are loaded. Your local computer shows as being
connected but this only indicates that it is connected to the host server,
not your work computer.

Cheers

Chris