i think you should not. two factors apply:
first, is there real background noise that you’re trying to overcome? noise canceling phones do their best work beating out constant, broadband noises like engines, so unless your fridge is really making you crazy, there probably isn’t too much of that kind of noise in your home to cancel.
second, the noise canceling technology necessarily changes the frequency response of the headphones, and therefore the accuracy. my wife has a pair of the top-of-the-line bose quiet comfort, and i brought them into my studio to compare against my sony 7506’s (the industry standard in film and theatre sound production). the sony’s are way more accurate.
of course, it’s all personal preference. the audio technica M40’s are more accurate than the sony’s, but i can work better with the sony’s.
try a pair, but make sure you can get a refund.