Atkins is a low carbohydrate diet where you eat foods high in protein and don't have to monitor your fat and calorie intact. One of the reasons it's thought to work is that by eating high levels of protein your siet is surpressed, or you feel fuller so you actually consume less therefore lose weight, if this is the case then yes eating meat for a week would cause you to lose weight though there are well publicised down sides to the atkins diet
without lowering the tone of the discussion, a side effect of eating ONLY meat could be humungeous constipation and if you didn't "go" for a week, you might not see a weightloss :-&
But would there be any point in trying this horrendous sounding diet? I mean it would be extremely difficult to stick to wouldn't it? As soon as you began to eat normal food again the weight would go on again wouldn't it?
also you'll fart like a demon and have halitosis! it works because it the lack of carbs stops your body making insulin so in order to keep going your body uses it's fat stores for energy. this makes you pee out protein called ketones which mess up your kidneys majorly in the long term. NASTY!