No, calibre must be running in order to run calibre and do one of the things calibre does.
What you can do, is set a schedued task (linux: cron job/systemd timer, not sure what the best way is with OSX but maybe launchd? Automator?)
Using the CLI backend, `ebook-convert` can take the name of a "News Source.recipe" as input. `calibredb add` can add the resulting ebook to your library, and `calibre-smtp` can be used to send files via an email relay.