I often see automated emails postfixed with a message like
*Please note: this e-mail was sent from an address that cannot accept incoming e-
No, there's no no-reply header.
no-reply
However, you can add an empty reply-to header:
reply-to
reply-to: <>
Which is valid according to RFC 5322, Section 3.6.2. Unfortunately, the RFC never actually specifies what an empty reply-to field means. I think most email clients just ignore it.