Hello -
My public school is looking into offering a game design course. I know Armory is an add-on for Blender and Blender is approved for use at my school. Github is not. Does adding Armory require sharing of additional personal information? Or are permissions run through Blender.
Hi and welcome 
As far as I’m aware* the add-on does not collect any personal information and it does not connect to the internet. What you do with your games is another thing of course.
* I’m absolutely sure about that, but I’m not a lawyer and this entire answer (and my following answers if existing) are no legal advice.
However downloading Armory from itch.io or cloning (downloading) the repository from GitHub might be tracked by those websites for various purposes, so if that is of any concern you should read their privacy policies. The same holds true if you update the SDK from within the Armory preferences panel, which will call Git in the background to clone the repository from GitHub. If you download a monthly Armory release from itch.io, you don’t need to use GitHub at all.
Feel free to ask more questions if the above isn’t specific enough :)
In order for the Armory3D armsdk to be updated with the latest Github source, it requires Git + internet access. The add-on itself is not update-able as I & @timodriaan discovered recently due to some memory/storage complications: https://github.com/armory3d/armory/issues/2473#issuecomment-1087800854
You can of course simply update the add-on/armsdk manually, but this is a pain as you’ll need to manually sync each computer with the new data either locally or via the school network.
If you are the teacher of the class course it’s possible you can allow your school network to allow students access to Github selectively per computer/student (a bit of a hassle).
Or… if you want a decent (but still complex) approach, you can run the Git + internet access via your computer and than sync your data to your student’s computer via the school network.