When publishing a post or page you can use the WordPress Visibility feature. Click the Edit Visibility link in the WordPress Page/Post Publish metabox and change it to Private.
Only logged in users will be able to view those pages/posts. Alternatively, you could try a lightweight plugin like Restrict Content. If I remember correctly it has a shortcode in which you can place the content that should be restricted and an option o display a login form if the user is not logged in. It’ll be the same user login as Connections users since it is the WP user that is validated.
Hope this helps!