All sorts of variables are at play here. Firstly, there’s the thermic effect of food, or the energy cost of digesting. Protein digestion uses a fair amount of energy, but protein intake doesn’t really change when people go keto. I don’t believe there is that much difference between the thermic effects of carbohydrate and fat, so that’s pretty much a wash.
Resting metabolism (BMR) can go up when the body gets extra calories, since processes such as the uncoupling of mitochondria come into play (part of the origin of the “meat sweats”). Also, in the absence of insulin, there is more metabolic fuel available, because ingested calories are not being shunted to the adipose tissue.
The brain is a huge energy sink, and someone lying on the bed thinking (say, a programmer working on a knotty problem) is actually using more calories than you might . . . think. 
Healthier mitochondria metabolize more. Well-developed muscles become more efficient and use less energy. But many people grow more muscle on keto—would that be enough to compensate for the increased efficiency?
Do ketones wasted in the breath or urine count towards the metabolic rate? They are literally “calories out,” after all! 
My guess is that it’s imponderable. The only way to know for sure would be to take several thousand people, measure their BMR’s before and after they go carnivore, and see if there’s a difference.