Can the low carb diet work?

Sure, but...: Those no carb diets all work by the same mechanism every diet on earth works by: less calories in. The key is that if you eat enough calories to gain weight but do it from fats and protein alone, it'll make you sick, so most people end up eating substantially less. Try it and see (myfitnesspal is a great app for this). Every 3500 cal missed (or so), another pound will fall off.