1/ Is it possible to make github/bitbucket your "local" repository, without having a local git?
No. GitHub or BitBucket repos are always upstream repo (top be clone), not local repo.
2/ How can this be done
From this thread, you can clone from a cloud9 console:
git clone git@github.com:whatever
That means you have a local repo on the cloud side (on the cloud9 server).
That is one of Cloud9 key features:
Version control is essential to every codebase. That’s why git and mercurial are baked into every aspect of your Cloud9 project, from creation to the command-line.
Rungit
andhg
commands in the command-line, just like you would on your local terminal.