Yes, you will still hear some outside sounds when music isn’t playing or it’s silent, though they’ll still be reduced in volume.
Noise-canceling systems listen to the outside world and the music you’re playing with small microphones, then use digital processing to try and filter out the sound of your environment by adding an opposite-shaped sound wave to your music.
When no music is playing, they still noticeably reduce the volume of the outside world but they can’t shut it out completely. They’re most effective against low droning noises and general environmental sounds, and less effective against higher pitches and nearby voices.
The effect is akin to turning the volume down on the world by several notches, as opposed to completely muting it.
Many retail locations offer demo kiosks that usually have a noise-canceling pair you can try to your heart’s content, though it will almost certainly come from one of the more expensive companies.
Thank you for reading, and best of luck to you. My girlfriend has a sibling who suffers from auditory sensitivity and I almost never see them without their headphones. I know that they don’t always help everyone but I hope you can find some relief.