Depends on what results you are hoping to achieve.
The research that inspired this diet used 600 calories of liquid meals + 200 calories of low carb veggies. It induced diabetic remission in 100% of the obese, newly-diagnosed diabetics. The follow-up study was less successful (somewhere around 50%, I believe), with high success in newly-diagnosed (<4 years) and much lower with longer-term diagnoses. A third study is in progress to see if it is as successful with home implementation (less monitoring).
If you are only trying to lose weight, 800 calories of twinkies will accomplish that – at roughly the same rate as following the diet. You’ll probably struggle more (a lot more) with sticking to the diet – since twinkies often trigger cravings for more twinkies.
The beauty of this diet (for most people who are unable to stick to diets without feeling starved) is that it removes/minimizes strong hunger triggers (carbs) and replaces them with things that make you feel satiated for longer (fats and proteins & to a lesser extent certain complex carbohydrates). [This is not universally true – for me, fats trigger cravings, as does the lack of carbs. So I actually struggle more with this diet than with other diets. I’ve learned to sort out which fats trigger cravings (bacon, for one) and avoid them. But it is largely true for most people]
They beauty for long term maintenance is that you can easily scale up the principles (what foods to eat lots of, what to avoid) to a higher calorie level because you are eating real, healthy, food. You don’t have to make a change to non-diet food once you reach your weight loss goal – you just get to eat more of what you’re eating to lose weight.
You might be better off in the long run by feeding your family this diet, perhaps supplemented by things you shouldn’t eat – and just eating less of what you are feeding them. This goes to the last point I made – this isn’t diet food. It is food everyone can eat and enjoy that would generally contribute to better health for all of your family.