Depends on the model. QC20's from bose (in-ear noise canceling) are basically magic in that regard - turn them on, add relatively quiet music, and I might as well be deaf to everything, including conversation.
That does lead the the annoying problem that I have to have something stuck in my ear (vs on, which isn't quite as annoying) for 6ish hours a day. Also, they're expensive af, and require frequent charging since I never remember to turn off the noise cancelling when I'm done with them.
Active noise cancelling systems generally only suppress continuous steady sounds, e.g. fan noise or motor hum. It actually makes conversations and other transient activities _more_ audible by reducing the background sound.