The amount people lose on the Atkins Diet varies, just as it does with any other diet. Some people might lose up to 14 pounds in 4 weeks, others might only lose 4. If you've been eating a very high carb diet (bread, potatoes, rice, cakes, cookies, potato and corn snacks, breakfast cereals, fruit juices, non-diet drinks, sweets etc) before you start Atkins, then you are quite likely to lose up to 10 pounds in the first week or two before the weight loss tails off to maybe two or less pounds per week. This is because you're using up your glycogen stores (intermediate energy stores) and as the glucose is burnt up, the water it is dissolved in is excreted. So what looks like a major weight loss is actually mostly water.
This water loss is a one-off, and you can't expect the weight loss it represents to continue. This initial water loss is what most crash or 'lose 14 pounds in 2 weeks' diets depend upon. 'Real' weight loss on the other hand is about changing your body composition, replacing fat with muscle to keep your metabolism as high as possible, so that you don't unwittingly go into 'starvation mode' and find yourself unable to lose any more weight despite eating less.
So, yes, you might lose what you want to lose in 4 weeks in terms of what the scales say, but you may not be celebrating the end of your dieting in just 4 weeks unless you only have a few pounds of 'real' weight to lose.