I don't recommend it for long term results.
I used to do that and stopped it, I always binged on the 7th day and felt sick the next day.
It would probably work for people who are already very lean and active. My dad eats fairly healthy most of the time, usually all organic foods. He's like 6'1" and 160 pounds. Hikes at least once a week, takes his dog for long walks almost every day. But, he likes his Eggo Waffles. And whose to stop him? He eats healthy most days, and even puts his expensive organic maple syrup on d'em Eggos.
Stumbled into Primal due to food allergies, and subsequent elimination of non-primal foods.
Start Gluten-Free/Soy-Free: December 2012; start weight 158lbs, Ladies size 6
Start Primal: March 2013, start weight 150lbs, Ladies size 6
Current: 132lbs, Ladies size 2
26lbs lost since cutting the crap.
I've had too many positive results to go back, even for a snack and I don't really miss any of those things.
My daughter did something similar, but she wasn't eating primal and was supplementing with protein powder a couple of times a day. One day a week she was allowed to eat anything she wanted, but she had to stick to the diet the other six. She did lose, but she also got tired of it.
"Cheating" on one's self is certainly CW mindset. Cheating on one's diet if one is eating 1200 cal/day to lose - omg I ate 1300! Now cheating on whom, Grok? If one eats an occasional non-primal food.
Cheating implies wrongdoing which implies guilt which means buying into the same old garbage about food we've been fed (pardon the pun) for the last 30 years.
If people had been eating predominantly wholesomely grown foods with the occasional snack or drive through meal, and if even non-processed food hadn't been corrupted by greed and ignorance, there'd be no need for paleo/primal/atkins/etc. The only reason we need these guidelines is that too many people started thinking that instant and over processed foods were okay for consumption on a regular basis.
Food is about many things. Nutrition, creativity, community, etc. Fanaticism and/or guilt over not towing the party line 100% has no place, imo, in the equation. It serves no positive purpose.
Even if eating non-paleo/primal one day per week, a person is 86/14. Sounds like a B+ to me; certainly not a fail.
"Right is right, even if no one is doing it; wrong is wrong, even if everyone is doing it." - St. Augustine