Is it possible to use the VSP Engine Tools post installer if my ArcGIS Portal and Servers are running within a perimeter network / DMZ (De-Militarized Zone) with restricted access to the internet via a forward proxy?

Yes, if your ArcGIS Portal and Servers are behind a forward proxy you can install the VSP Engine Tools. However, it is necessary that the correct HTTP and HTTPS proxy URLs with optional proxy credentials are accessible by the post installer.

In Windows a forward proxy is generally configured by adding appropriate Windows environment system variables.

For example: HTTP_PROXY = 'http://myuser:mypass@[IP address]:port' and HTTPS_PROXY = 'https://myuser:mypass@[IP address]:port'.

Another way might be to configure the proxy manually or automatically via a Windows settings dialog in Network & Internet > Proxy. If a correct proxy configuration is available on your host, the installer should be able to detect and use the settings for the publishing process. Similarly, the proxy settings should be available during VSP Engine Tools Task executions on the ArcGIS Server where they are installed.