It happens all the time. I remember Chuck Yeager in his biography saying he did it all the time when flying cross country (not while being a test pilot though).
This is why we are hearing speculation from so many pilots that the crew fell asleep. They've done it themselves or know of other pilots who have.
Let's just say, I doubt it. If ATC calls and you don't answer, you're not going to be flying for very long. I suppose if you have a really good autopilot (which I never had) which does navigation across waypoints, you might be able to claim radio failure once or twice and get away with it.
There is just so much wrong with this story. When I'm flying commercially, I am usually quite aware of where I am if I can see the ground. Going into Newark here from anywhere in the US, being out over the ocean would sort of be a big clue that something was wrong. My guess is that Minneapolis, or wherever they were going, gives similar "clues." Even if I cannot see the ground, I know when the plane should be descending. And even if the crew was clueless, I find it surprising that no passenger tried to find out what was going on.
ML/NJ