When I was younger, I spent hundreds of summer nights in the southern Appalachian backcountry, both on and off the AT, and during this time I pretty much tested the limits of not protecting my food at night (don't ask me why, it's a long story).
My empirical observations were as follows:
Probability of getting my unprotected food bags nibbled on by rodents while camped in a "stealth campsite" - 5-10%
Probability of getting my unprotected food bags stolen by bears while camped in a "stealth campsite" - effectively zero
Probability of getting my unprotected food bags nibbled on by rodents while camped in an AT shelter - 95%
Probability of getting my food bags (carefully hung on the makeshift food lines inside shelters) nibbled on by rodents while camped in an AT shelter - 5-10%
I never had a problem with bears, although admittedly, I also almost never camped in well established backcountry "campsites."
The one exception to my bear experience was in the Great Smoky Mountains National Park. In that park, you are forced to camp only in designated campsites, and the park is filled with scavenging bears who know what they are doing and will frequent the campsites specifically to look for food (I saw a few of these guys in person). All my food was always hung a la the park rules and I never had an incident where a bear (or rodent) got into my food.
If I were to hike the AT now, I would hang my food every night and avoid shelters wherever possible. They are infested with mice and other hikers who smell and have weird habits (because, let's face it, that's everyone out there, including you).
If you are camped in a stealth campsite and want to keep an energy bar in your pocket at night while you sleep in an enclosed shelter of some sort, then I would say you are most likely going to be fine.
If you are camping in shelters or in lots of well used campsites, then all bets are off. I would not sleep with my food in those instances, that's just asking for trouble.
Just my two cents.