Do Exchange Auto-responders Reply To Auto-responders

I have an address that receives hundreds and hundreds of e-mails a day. It's an address people aren't supposed to use (basically noreply@mydomain.com), but people do. I'd like to stop being the guy that gets these and routes them as appropriate, but we can't just turn it off and cause a hard bounce, because that will bewilder too many people who don't get that replying to noreply@mydomain.com is a bad idea. (Our website sends out notifications to people. A lot of people reply for various strange reasons, and we also get a lot of autoresponders sending us junk.)

I'm a Linux admin, so I'm a bit out of my league -- this needs to be configured on our Exchange box.

What I'd really like is an auto-responder for this address that will tell people that they e-mailed a mailbox that no one uses, and give them directions on how to contact a real person if need be.

However, fully half of the e-mails we receive are people's auto-responders. Is an Exchange auto-responder going to reply to their auto-responder? This will completely bewilder people.

And if this will auto-respond to auto-responders, is there a cleaner solution here? Again, it's got to be Exchange, but I'm a Postfix guy, so I have very little experience here.