Even if you are not connected, you should be able to use Audirvāna Studio/Origin. If it’s not the case then there is an issue on your device with the login process.
You then need to disconnect and then reconnect your account. To do this you need to go to Audirvāna Studio settings, My Account section. After doing this make sure Audirvāna Studio/Origin are starting properly without asking you for login.
After doing this, please make a test by closing Audirvāna Studio/Origin and then disconnecting your computer from Internet. Do you get the login window when you start Audirvāna Studio/Origin ?