No. It is not necessary to turn Dante Virtual Soundcard off when you power off your computer.
The Dante Virtual Soundcard application acts like a control panel, allowing the user to configure and enable the software.
Dante Virtual Soundcard will show up as a soundcard in your audio settings. Once the application window is closed, Dante Virtual Soundcard continues to function and be available, even if the computer is restarted.
More info here: Starting the Dante Virtual Soundcard Control Panel