My autocomplete and documentation work offline. Not being able to download new libraries would suck, but as long as you have the necessary tools installed it wouldn't be too bad.
It's not that long ago that software was distributed on CD and tutorials in printed books. The internet adds a lot of convenience and productivity, but it's hardly a requirement.
Most open source projects are the work of one developer with occasional outside contributions. Those can still be distributed by CD or USB stick, either directly by mail or the more traditional route of magazines having CDs with collections of software their subscribers might like. Or a modern version of people meeting up to exchange files peer-to-peer. If you want to contribute, write a patch and send it back to the developer, e.g. by snail mail.
Large open source projects would be much more difficult. Though some of them are already either largely done by one company (so people can meet in person) or very hierarchical (like Linux).
To be honest, I would expect most small open source projects to just vanish, because of the lack of discoverability. The users won't be able to test them easily, and probably won't be paying for the shipping of a tiny tool that they have not yet tried and don't know whether it's useful or not.
Large open source projects can survive, but I'd imagine it will lean much more towards being developed mainly singular organizations. Without the internet, we don't just lose contributors, but also a lot of testers. The feedback loop will probably shrink, such that the software is mainly based on the need of the organization itself, and the perhaps a selected few collaborators who are very involved.
The entire open source ecosystem will be gone. Distribution on CD (or USB sticks) would be okay for delivering software, but not viable for frequently exchanging patches among a large group of developers in different parts of the world.