Anecdotally it seems this depends a lot on the individual. Based on the actual studies I've read about (though I'll admit this is interpretation by science journalists rather than my reading the studies myself) this would generally be a very unproductive extra two hours, and would also cause a large chunk of the rest of your day to be less productive for mentally challenging tasks (the only kind I'm generally concerned about). That last point is why the kids argument doesn't seem to fly for me. When you have a baby that wakes you up every couple of hours, the tasks you are doing are routine, and man parents do it barely being conscious.
Oh damn now he's puked all over the laptop dammit. Eugh he has spots on his ear wonder if that's ok. Oh great now the nappy has exploded. Oh great now this bottle leaks.
But granted, some of it you can do semi conscious.
of course I meant most of the time. Of course they'll do things to jar you to full consciousness (good or bad). If they were that routine, who would want them?