Nope. Tried this earlier this morning and the server rejects any pushes:
ERROR: This repository was archived so it is read-only.
fatal: Could not read from remote repository.
Please make sure you have the correct access rights
and the repository exists.
This is interesting, and not something I'd considered!
Edit: The only downside that I've neglected to mention is that leaving GitHub entirely means losing support of being listed in Swift Package Index unless (or until) they support reading from GitLab as well. Last I knew, they only support GitHub hosted packages right now