Thanks for your inquiry.
Yes, your scheduled emails will be delivered even if your computer is off at the scheduled time. Only if you have switched Compatibility Mode on in order to make Send Later work for you, you do need to leave your computer on.
To find out more about the Send Later feature, please see here: https://support.mailbutler.io/knowledge-base/send-later/
To find out more about Compatibility Mode, please see here: https://support.mailbutler.io/knowledge-base/compatibility-mode-for-send-later-and-snooze/