Can you send notifications in ServiceNow without creating a notification record in the notification table?

that's right, with the "GlideEmailOutbound()" method, you can send email notifications directly from your script without additional records.

var email = new GlideEmailOutbound();

email.setSubject('New Task Assigned');

email.setBody('A new task has been assigned to you.');

email.addRecipient('[email protected]');

email.save();