No, there’s no existing function available for an equivalent UI for posts or pages.
The whole UI in your screenshot is provided by the post_categories_meta_box() function, which uses wp_category_checklist() internally for the actual checkboxes, which implements the Walker_Category_Checklist class. All of these are built for listing terms as checkboxes, and can’t be repurposed for listing posts.
You would need to implement this yourself (although if you look at the source for post_categories_meta_box() you might be able to use matching markup to ensure visual consistency.