Noise canceling does indeed work when not playing music. I don’t know how long it stays in that condition, but I know it starts the canceling as soon as you put em in your ears. I have done this for at least 5 minutes without playing any music, so I’m pretty sure they’ll keep cancelling noise, just don’t know if they turn off or sleep at some point due to ‘inactivity’
I am not picky about sound quality, so it’ll be difficult for me to respond to your other question.. I did own Bose QC 35s and have now upgraded to the new NC700s, I don’t think it’s a fair comparison though. I don’t think you’ll ever find earbuds that sound as good as over-ear headphones.. IMO they are in a completely different class.
I do own other earbuds like Bose Soundsports and Zolo Liberty +, these AirPods sound as good or better than any earbuds I’ve ever worn..