The Airport ride is the only consistent ride in Atlanta I know that has a proper nature break. After about an hour in, and 3 to go, the peloton stops and riders line the sides of the road to take a leak and have a bite to eat. I believe the secret handshake ride Kellytown has one, and I believe Silk Sheets does as well (I don't like doing rides I have to drive to though, so Silk Sheets is off my list).
I think the nature break is a great thing. Especially if you like drinking coffee in the morning (I do). If you know it's coming, you can be a little more aggressive about hydrating, knowing that whatever is in excess you'll get rid of.
In general I'd say any ride that's 3 or more hours should have a nature break of some sort. Otherwise you get guys pissing on the side of the road at stop lights (like happens at Tucker from time to time).