Absolutely. My 20-carb diet (which took me, a petite 5'3" woman from 150 to 125 in five months - THANKFULLY) was as high as I wanted it to be in calories. But I didn't feel hungry. No cravings. What glorious freedom - to enjoy food at meals and not feel hungry! My stomach would actually growl, and I'd think - "oh, it must be hungry," but I was fine with that.
I had been a horrible 150 for three years no matter what I tried.
If I had hours a day to work out, I might lose the effects from carbs. But I'm not a professional athlete, and I don't have the luxury of time - I have children. That said, a few minutes of exercise a day is incredibly important, of course.
That said, I am not in favor of the government prescribing any diet advice. That is a dreadful course that we've been on since George McGovern went on the Pritkin diet and decided it would be good for everyone to stuff themselves with bread and feel guilty about fats. He's a mass murderer.