I don't think so - your body will start burning protein instead, so you lose muscle instead of/or as well as fat. If your metabolism is getting No carbs and No fat (or very little) then all hell breaks loose (just like it did in our caveman days when there was no fat available).

I eat heaps of fat, and am still losing both inches and weight and cholesterol points very nicely. Atkins warns against the low fat approach.

Right at the moment I'm tucking into my low-carb jelly and double thick cream!