If your clients want to send do-not-reply emails...

Don't let them send it! This post by Seth Godin talks about the wasted opportunity and aggravation caused by companies requesting recipients 'do not reply' to the email just sent. If it's important enough to send, surely it's important enough to acknowledge and respond to emails about it. You can create a reply-to email that may go to a group of people who can respond to it. One thing he doesn't mention however, is if your client sends out an email that could elicit responses, to put on adequate numbers of (temporary) staff to handle the influx.