I’m not sure how you are defining “successfully” in this context.
I was just reminded the other day that a ketogenic diet was the original standard treatment for Type I diabetes. It only fell out of favour after the development of insulin treatment in 1923.
I can’t imagine that any diet would keep someone alive for too long in the complete absence of insulin, but Type I’s today still say that you can prolong the “honeymoon” period (i.e., the phase after the development of symptoms, but while the pancreas still retains some ability to secrete insulin) by means of a ketogenic diet. And before the discovery of insulin, a ketogenic diet was probably the best hope of avoiding a fatal increase in hyperglycaemia and preserving the patient’s life for as long as possible.
In the case of Type I, it is not likely that anything can keep the immune system from ultimately destroying all the β-cells, but in the case of a late-stage untreated Type II, there is probably no reason that the pancreas couldn’t (slowly) recover, at least to some extent.