Type1 diabetic and atkins?

Im a type 1 overweight diabetic,and I would love to start a low carb/atkins diet but will I loose weight if the aim of these diets is to get ketones and I cant do that.Also an aim is to lower your insulin intake I wont have to bolus for my meals as there will be no carbs but I must continue taking my basal which is about 20u per day.What is the amount of insulin a pancreas would produce in a non diabetic on this diet......Are there any diabetics who have succeded on this diet or any other diet I AM DESPERATE!