Carbs soak up water, so it's natural that you would gain weight when adding carbs and lose weight when you remove them. That's why doctors and nutritionists say not to worry about your weight, but worry about your waist. Weight can be misleading.
The amount of carbs stored in the human body would not account for 100 lbs, not even for 20 lbs. A couple of pounds of carbs are stored in the body, in the form of glycogen, plus the water it soaks - maybe three times more, so the difference may be about 8, maximum 10 pounds.
I would certainly worry about 20 lbs gain, carbs or no carbs.
Yes. The only way the carbs are stored in the human body is in the form of glycogen, in liver and skeletal muscle. There's about 1 kg of it in total, maybe a bit more if you're a trained athlete. And glycogen binds about, maybe, up to 3 times as much water by weight. So, altogether, about 4 kg.
After switching to keto, glycogen is used up gradually, due to no carbs entering the body. And the water is also lost. Therefore, the "signing bonus" of the keto diet - a significant weight loss in the beginning, but due to water lost, not fat burned.
BUT. That only accounts for about 4 kilos, maybe just a bit more. You can't really blame water for a gain of 20 pounds.
No one ever said it could account for 20 lbs. Merely that you should expect weight loss when you're cutting carbs and weight gain when you reintroduce carbs.