Answer
Not through configuration alone — out of the box, the Customer History tab's content isn't something you can change purely through the UI or standard setup. Adding to it (for example, capturing additional business events into the history) requires custom code, typically a custom API that populates the history table in the background for the specific events you want tracked, plus custom fields or custom RMB actions added to the tab itself if you want to view or act on that additional data from there — none of this is available as a native, purely-configurable option.