Atkins is a ketogenic diet. I've never heard of anyone taking days to "carb up" on a ketogenic diet, but I haven't heard of everything, and the Cyclic Ketogenic Diet apparently takes this approach. A very high intake of carbs will stop the ketosis and switch you back to carb-fueled energy, and it typically takes 3 days to switch back to ketosis. The amount of carbs generally needed to make the switch as I understand it is somewhere more than 9g of carbs in less than an hour, depending on the person and how their body processes the sugars.
Atkins dieters usually go heavy on the protein, and there's ample research that shows that excess protein is extremely bad for you. Your body will leach calcium from your bones in order to flush the excess from your body. Your body can handle more protein without losing calcium if you are working out fairly heavy, but still not enough to cover as much as many of the people I've seen on Atkins take in.
Fat, on the other hand, is turned into ketones for energy, and is then either burned or flushed from your body in sweat, saliva, urine, etc.
In summary, the higher protein intake is much worse for you than the higher fat intake if you are NOT working out. Whether or not extended periods of ketosis are bad for you in general is still a matter of debate.
Referring to AlexC's answer, losing weight and keeping it off requires a lot more than just going on a diet for a while. It requires a dedication to a lifestyle change, including exercise and long-term healthier eating habits and goals. It's well worth it, though, your moods will be better, you'll sleep better, feel better, etc.