You can. It's very doable. Plenty of people do it.
But the real value of GH was "social coding" - open public access to open public projects.
That's going to fragment, even if GL takes over. And that will be a loss.
The real problem is the lack of open public server infrastructure. In the same way that everyone has access to a browser, everyone should have access to a private server, which is secure-by-default, controllably networked, super easy to set up with a selection of server apps that include social, commerce, payments, and public/private sharing of various kinds, and cheap to run.
The centralised consumer internet - where servers are far beyond the skill level of most users and can be a nightmare to set up and administer, even for professionals - is one of the reasons we have giant predators like MS and Facebook.