If anorexics suddenly eat 2000 calories in one night will they gain weight?

Not exactly. It takes 3,500 extra calories (that you do not burn off) to gain one solid pound of weight. If you eat that many calories, which is probably a considerable amount of food, you will "gain" weight quickly. But most of that is the food and drinks still in your body. That will naturally go down in a day or two as it passes through and out of your body. Also, it does take energy (burning calories) to digest foods, too.