It really depends upon the frequency range of her voice -- if she's hitting all the highs and lows simultaneously (like in the white noise from a fan or engine), the ANC may be helpful. If she's only emitting a few frequencies, it's the pads of the headphones that will be helping reduce this noise more than the ANC. Unfortunately for you, the best way to reduce the noise from your wife's nagging is to take your headphones off and help with the dishes.
If she nags around 70 decibels and she’s right up in your face you will be able to hear muffled nagging. However you can just act like you can’t hear her. If you turn on music or sounds along with the noise canceling you probably won’t be able to hear her nagging.
With an issue like this, I tend to blast the spund. Just last week I didn't hear a peep of the gunshots in my street and boy am I glad I got these headphones or else I would've crapped myself. Overall, yes, it should drown out the most livid sounds you can think of including the siren wale of a nagging woman.
Life must be a bitch with a nagging wife. I am not buying these for that reason. I married a non nagging angel ! I feel for those of you that have one of those unfortunate squeaky creatures at home.....