Like with every diet, the outcome will depend on many factors.
One of the factors would be how much sugar and starches you have been eating before the start. You might experience a condition similar to what you would have if you stopped smoking or drinking coffee. It is not probably that sugar is addictive by itself but high carb diet makes release of "pleasure" chemicals in the brain easier. When you eat high carb diet or crave sugar, you are getting used to higher levels of dopamine in your brain and can star feeling bad when you lower your sugar intake. It does go away for most people. It will be the same on any diet Atkins or not if you cut sugar significantly.
Many of us have overgrowth of candida and yeast that thrive on high sugar, high carb diet. When you cut the supply they start to die, which is a very good thing. But it may cause flu like symptoms for a couple of weeks, while your body gets read of the toxins.
You start losing fat fast, fat cells is where your body stores toxins. Once they get released into the blood you will again experience flu like symptoms. How much again depend on how clean your diet was before you started. Drinking more water can help with flushing the toxins and extra ketones out of your blood stream.
On Atkins you are trying to switch your body to burning fat, vs burning only carbs. For some of us it is more difficult to do. It takes 2-3 weeks to adjust, hence the induction. How rough it will be pretty much depends on how bad your dependency on carbs is. Burning fat and proteins for fuel is normal, it is just that some of us fed our bodies so much carbs that there was no need to do it before.
You can feel less energetic on any diet. You are creating energy deficit to lose weight, of course you body resists at first. You need to lose some weight first before you can start feeling more energetic.
Please also keep in mind that while some people give up, some people feel so much better on low carbs, that they never want to go back to high carb. That is why so many people become advocates of the diet.
Very low carb are only applicable to induction. After that you can start slowly increasing the amount of carbs to the level your body can tolerate well. One of the issues is missing your favorite food, try to find new food items and recipes that you can enjoy, there are plenty.
The first thing you lose on a diet is your sense of humor. ~ Author Unknown
It doesn’t matter what diet you follow… What matters is what makes you follow your diet. ~ Tom Venuto