Rarely... it is much more likely to be accompanied by blood glucose over 13 mmol/l.
I am of the understanding that the absence of insulin causes the body to burn fatty acid's the by product of that is keytones, lack of insulin also causes fatty tissue to release fatty acids.. high blood glucose (due to lack of insulin) causes the body to urinate frequently in an effort to remove glucose from the blood.. this urination causes dehydration and the loss of essential electrolytes. Eventually you run out of body water to remove sugar and keytones from the blood.. keytones are acidic and if they aren't being removed then your blood acidity increases... causing all-sorts of unwanted problems.
On a low-carbohydrate diet it is perfectly normal to have some keytones in your urine.. as long as you are well hydrated and your blood glucose is below 13 mmol/l then I don't think it's anything to worry about.
Edit: info provided