Yes you can install without INet. Under the hood an ADS extension is just a VSIX file which is the same thing that VS Code and Visual Studio use for their installers. You can copy this file to any machine you want. In ADS go to the Extensions view and click the additional options (...). At the bottom is an option to install from a file. Alternatively, at least in VS, you can double click the VSIX file directly and run the installer that way.
The hard part is getting the VSIX. I think it is just downloaded temporarily so capturing it might be hard. Never really tried myself. But a VSIX is a zip file and it gets extracted to your AppData...AzureDataStudio folder so you can go there to get the contents of the zip. In theory if you zip this back up it should be good but I've not tried that. As long as the manifest file is there then it should install fine.