It could still be identified as the same codebase by eg. comparing commit hashes or content hashes, but that's harder. If you really want to be sure, clone the repository, make a few local edits to files (eg. adding a comment to each file), copy the full source repository to a new directory in the filesystem, git init that as a new repository, commit changes, and push. That blows away all the existing history of commits, and ensures that each file has a different hash. It's still technically possible to detect it as a dupe, but would require an extremely expensive shingling or filesystem diff on every repository in GitHub.
Wouldn't a GitHub search still find it pretty easily? As I understand it, they put significant effort into supporting search; but since that's being done anyway, it doesn't have a very high marginal cost.