I don't think it would make much difference, to be honest.
It takes anywhere from 2 weeks to 2 months for a person to become ketoadapted. The time depends on a lot of different factors, including lifestyle beforehand. That means that even if you crash into fat burning by a water fast or a fat fast, or just go low carb, it still takes weeks for your body to learn how to switch fuels efficiently and be comfortable in ketosis.
You may deplete your glycogen reserves quickly, but it doesn't mean that your body had learned to get the best out of fat as a fuel. That takes time.
During the transition is when you are likely to experience the symptoms of 'low carb flu'. some of the symptoms are easily dealt with - more water, minerals, etc. Others are just inevitable - brain not as focused, tiredness, etc.
My experience is that carb flu is easier the fewer carbs you were eating beforehand, and it gets easier the more times you go through it.
I think it is also fair to say that fasting is easier if you are in ketosis before you do it.
But you can try it and see.
