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Your body can run on either glucose or ketones. When you follow a low carb, high fat diet your body uses a higher percentage of ketones as energy (derived from fat). It's a much more stable form of energy since it is a constant and even supply instead of the spikes and lows from traditional carb heavy diets.

If you are referring to gluconeogenesis, yes, fat and protein can be converted to glucose but the amounts are fairly negligible. If you eat fat or have fat the body will convert the fat to ketones and use that in the absence of glucose. It's a much more efficient metabolic pathway than going through gluconeogenesis. The vast majority of the body functions quite well on ketones for energy. Most people are not able to metabolize fat at the rates required to avoid fatigue without undergoing ketoadaptation though. It takes anywhere from 3 days to 3 weeks depending on the individual and seems to be correlated with insulin resistance.