As you are not taking medication you should not go low - unless there is something long lasting in your system - but even that should be reducing in its effects.
Your liver should break down fat to supply your needs, but a continued fast might result in muscle loss.
I doubt that prolonged fasts are any better for a diabetic than occasional shorter fasts - once you have reduced the most easily accessed energy sources from blood and the liver's glycogen stores you have begun to push your metabolism back towards more normal behaviour, but going on longer might not give any better results.
It might in the end be detrimental, as loss of muscle is not helpful, quite the reverse, as muscle uses up energy just by being there. Maintaining muscle mass is important for many reasons.