Should I use the Reply-To header when sending emails as a service to others?

I tested dkarp’s solution with gmail and it was filtered to spam. Use the Reply-To header instead (or in addition, although gmail apparently doesn’t need it). Here’s how linkedin does it:

Sender: messages-noreply@bounce.linkedin.com
From: John Doe via LinkedIn <member@linkedin.com>
Reply-To: John Doe <John.Doe@gmail.com>
To: My Name <My.Name@gmail.com>

Once I switched to this format, gmail is no longer filtering my messages as spam.