Would I have to do anything special aside from installing an older version? I’m not familiar with the back end of pip - in particular whether it talks to a package server or not.
I get expecting that everyone will do this on their own, I just don’t think it will happen that way.
In addition, paid extended support for Python 2.7 already exists from 3rd party vendors (I know of ActivePython) - Python 2 EOL just means you don't get free updates and supports.
For those cases you will want to make sure you have a local mirror.