In general, SBD is a very healthy way of eating, and you can lose weight and see overall improvement even eating quite a lot of food. It is important to control the portions of some calorie-dense foods, but others (especially vegetables) are unlimited. People are often surprised at the big quantity of food they eat, and that they don't go hungry.
I recognize that "binge eating" means different things to different people. To some people it just means they enjoy eating a lot of food. To others, it means eating past the point of satiation, like an addiction. SBD is just a healthy way of eating, not a cure for addictions (although some people here have said it brought their unhealthy eating patterns to the forefront). There may be other issues involved in binge eating that I'm not aware of, too. I would suggest you talk it over with your doctor. He or she is in the best position to decide whether something else in addition to (or besides) SBD is a good plan for you. Best of luck to you!