I've managed to do an unattended install by using the following command line:
VSCodeSetup-ia32-1.13.1.exe /verysilent /norestart
But this launches the application at the end of the install process that I'm still trying to avoid. Executing the setup /? lists all the available options but none seem to cancel the application launch.
Setup Type: Windows Installer (Delivered as an EXE)
Deployment Method Used: Vendor Provided Command Line (switch driven)