No, we would continue to use Github for the foreseeable future. If a FSF hosted Gitlab/Gitea/... instance came to be, then we would likely switch to that.
Also I am not exactly a fan of either the git forge or the mailing list work-flow. So I plan to add "competitive collaboration tools" to Magit that allow a project to continue to use either back-end while also allowing all or some contributors to use collaboration work-flows that are more tightly integrated with the development and version-control work-flows. https://github.com/magit/magit/issues/2972
The primary downsides of assigning copyright to the FSF that I see is the "waiting for papers to be signed" part and that some potential contributors will no longer be able to / be willing to contribute.