No, we are not aware of anybody running its own Studio server. It would be possible as all the sources are published and online, but I can’t think of the amount of time that deploying it and getting all the content could take.
For the problem you mention, other people are either
a) preparing a server with the desired content and cloning its whole disk (using tools like https://clonezilla.org/ )
b) Using the methods kolibri provides to load the resources without an Internet connection
If you have sysadmin skills, a) is quicker but it’s harder.
Fo normal users, b) is the easiest method. With b) you have two alternatives:
In an Internet connected location, install kolibri, download all the content you need and export it to an USB drive that you can take wherever you need. Then, import the content from the USB in a Kolibri server without an available Internet connection. It’s a described procedure at https://kolibri.readthedocs.io/en/latest/manage.html#import-content-from-a-local-drive
Using a laptop, install Kolibri on it in a location with Internet access, download there all the content you need. Then you can take the laptop to any kolibri offline installation, and connect it to the same LAN where you have your empty kolibri server. In this empty server you will be able to autodetect and use the laptop as a content source. It’s a kind of portable Studio installation for all intents and purposes. It’s a described procedure at https://kolibri.readthedocs.io/en/latest/manage.html#import-content-from-a-local-network-or-internet
You have also a complete tutorial at https://kolibri.readthedocs.io/en/latest/install/tutorials/provision.html with all these options, explained step by step.