The automated plugin keeps track of posts. If there’s no new content, the newsletter is not sent (unless you explicitly force the plugin to generate it regardless).
That being said, we have a similar problem: sometimes (quite often, actually) we publish some important posts that our subscribers should be notified about promptly. They can’t wait the end of the working day to receive the daily newsletter. The newsletter plugin does not provide any feature that could allow that. Other plugins do, but they do not “talk” with the Newsletter plugin, specifically its channel/list of subscribers.
So I am stuck.