ANR headsets DO NOT protect your hearing. A former student is an Ear, nose and throat specialist and said most of the noise you get comes through your skull. Plugs and a good passive cancelling headset help, but ANR really doesn't do anything to physically protect your hearing. You still get all of the noise pollution though the ANR headset.
However, they do a great job reducing fatigue. That helps your hearing as much as anything I guess.