From Projects-Cleanup we archive a repository by marking it Read-Only but that does not prevent it from being replicated to GitHub. Once a repository is archived in Gerrit, I don't think there is much point in replicating it to GitHub.
The replication plugin would only replicate repositories that have the READ permission set for the special authentication group mediawiki-replication:
profile::gerrit::replication: github: url: 'git@github.com:wikimedia/${name}' authGroup: 'mediawiki-replication'
The permission is granted from All-Projects.git:
[access "refs/*"] read = group mediawiki-replication
Thus tentatively, we can create a new permission repository All-Archived-Project which would take away the READ permission from mediawiki-replication group by creating an access rule BLOCK. Then when we archive projects, we would reparent them to that All-Archived-Project and they will no more be replicated to GitHub.
We might also be able to block changes to refs/meta/config to anyone but Administrators and Gerrit managers to prevent owners from restoring a repository. But that is another topic of its own.