Effectively. My project still gets pushed to GitHub and lives there, but I've disabled every feature I could (you can't disable PRs, but it's easy enough to redirect PRs over to GitLab).

Code Climate can still happily read from the GitHub project and I can add the badge to the README if desired, which is visible on both GitLab and GitHub.

And since origin pushes to both, they are rarely if ever out of sync.

And by using GitLab I get GitLab CI instead of Travis (which is quite nice), GitLab's amazing Issue tracker and board, which blows GitHub away, more fine grained control over merging (no more forced --no-ff merges if you don't want), Issue and MR templates, an activity stream, far more control over your project's settings... really I can't say enough good things about my experience with GitLab over the last ~6 months.