If your local server is still serving the old files from wp-content/uploads, then no action is required: old files will be served from the filesystem, new uploads will go to GCS. However, if you want to migrate the old files to GCS, you will need to upload them to your GCS bucket, and also rewrite all references to them in the WordPress database wp-cli can be handy for this). Note that the database records are quite fragile (the media metadata uses PHP serialization) so this can be a tricky process and you should backup your database first. You could also manually recreate the media library by downloading then re-uploading each image through the admin database, and then manually updating the old posts (which will be a lot of work, but won’t corrupt your database!).
Also, as of v0.1.6 of the plugin, uniform access control should also work.