Calibre runs on your computer. So, in order for it to do anything at all, the computer must, of course, be running. You can, however, automate the task of downloading to require no user interaction whatsoever. Search for batch downloading via ebook-convert, then automate it using the facilities of your OS to run at system startup. After that, you only need a way to get your computer to automatically start up at a certain time and shut down again after the download and send is finished.
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