This question has probably been asked/answered a thousand times, but i couldn’t come up with a good answer when my client who is a nutritionist raised concerns about what happens to your body after a fast. Meaning, since your body is going without food, does that mean when it gets food, it is more prone to store the energy (fat) for the possibility of future famine.
Tell me exactly how wrong she is. please.
There are likely more experienced and knowledgeable people to answer this question…but here’s my understanding:
Insulin is what controls the storage of fat. When insulin goes up, your body says - hey hey now! Look at all this delicious energy coming in. No need to use our fat stores now; in fact, we can store this incoming energy for when we need it! Because eating ketogenically drives insulin down, your body is not encouraged to store fat. Granted, protein will create an insulin response, but not nearly as high as carbs. So to answer your question, no. 
This week’s episode of Obesity Code podcast does a much better job of describing this than I am currently doing.
I agree with the above. And also add it sounds like the nutritionist incorrectly thinks your metabolism slows while fasting (“starvation mode”), but it doesn’t, it ramps up, at least for a few days. So if you are fat adapted, and your insulin is nice and low from fasting, when you eat again you will use the energy from fat rather than storing it. and the protein you eat will go to build up the things protein builds.
If you want to slow your metabolism & make your body pack on weight, eat 1000 calories spread throughout the day, mostly carbs.
This brings forth the next question. …since the metabolism increases, does it then stay at the increased level? Indefinitely barring any stupid eating? A few days? Until the fast is broken?
The things that seems to slow metabolism, from all I’ve read and heard, is eating too few calories per day, over many meals per day, for a while. And homeostasis, the body, getting used to the level of calories coming in and adjusting energy output to match. What seems individual is how long you can extended fast before your metabolism slows.
So IMO, switching it up with caloric intake, fasting, and eating within a window are all methods of keeping metabolism revving.