no, this is GitHub packages, not GitHub repositories. Cargo doesn't use this. It doesn't use GitHub repositories either, they store the crates internally.
EDIT: I was wrong, the crates index does use a GitHub repo
The crates.io index actually is a GitHub repository, so I think a GitHub outage that affected repositories (not just packages) could break Cargo. Only metadata is stored there, though, not the actual crates. I'm not 100% sure why it works like this; there seems to be a plan to change things soon so that Cargo running on users' machines doesn't talk directly to GitHub by default (https://blog.rust-lang.org/inside-rust/2023/01/30/cargo-spar...), though the GitHub repo would still be the source of truth.
crates.io also uses GitHub as an OAuth provider (and it's currently the only one offered), so if that broke then people wouldn't be able to publish crates, though downloading existing ones would presumably still work since you don't have to log in to do that.
That's being addressed with a new index protocol, specified a while ago[1], available for testing since the middle of the last year[2], and slated for release in a week's time[3].
crates.io also uses GitHub as an OAuth provider (and it's currently the only one offered), so if that broke then people wouldn't be able to publish crates, though downloading existing ones would presumably still work since you don't have to log in to do that.