Is there any way to modify the mail headers in an outgoing message sent using Gmail? I'm interested in doing this to add an "Approved:" header to a Mailman announcements-only list (reference).
If you are using the Gmail web interface the answer is no, it's not an available option. However, you can bypass this restriction by sending an email using a script or any other tool where you can control the headers and using the Gmail SMTP to deliver the message.
Every programming language allows you to write a script to deliver an email. There's also a ton of pre-packaged scripts you can download, install and customize. Make sure to use Gmail SMTP so that the email will be stored in your Gmail account.