Competitive eaters throw their food up and keep it secret as "I'm just calorie counting" sounds a lot better than "I pretty much have an eating disorder". You can't eat large portions once a week and still train your stomach to stretch enough to eat those gargantuan amounts of food that they need to perform.

Some do this, some go on binge fast cycles. Others just eat the food. It's different for everyone. Binge fast cycles are probably the easiest way to train this though.