This is a normal usage of Chocolatey, completely disconnected. Most companies set up their own servers (as you have noted) and make their own packages or pull in and change packages to look at local resources instead of the internet.
We are going to be getting better at making Chocolatey proper able to handle this. The process of taking an existing package and editing it so that it is completely offline is what we call internalizing - see https://chocolatey.org/docs/how-to-recompile-packages. And Chocolatey for Business offers Package Internalizer - https://chocolatey.org/docs/features-automatically-recompile-packages