Given that a malicious party gains access to a GitHub repository, would it be possible for the adversary to delete or modify versioning information / history after she altered code stored on the repo? Is it possible to always detect such code changes after a compromise of a GitHub repo?
The most damaging thing someone can do to a GitHub repository is to delete it. With enough access they could then create a new repository with the same name. After that, anything they wanted can be different from before.
Git lets you sign commits. Making and verifying those digital signatures is a good way to assure yourself that the changes retain integrity.