A set of one of those will probably do the job of lessening voices to something acceptable--they do to the point that my very, very distractable self can work in an open office, whereas older NC headphones did not--but they won't completely remove it.
If you really want that, I'd suggest a set of 34dB+ reduction earplugs. If that doesn't work, put them underneath NC over-ear headphones. If that doesn't work, play white noise on the headphones. I'll be surprised if you heard anything external after that.