Just to talk about having energy while exercising, the answer is yes! On a Very Low Carb Diet (or a Low Carb, High Fat diet), a person is in the state of ketosis. Ketosis is a state where the body has no glucose (carbs) to burn for fuel, so the body switches to using fat for fuel. For that reason, to keep energy up on a VLC diet, many of us eat 40-60% of calories from fat!
Many scientific types also believe that in a ketogenic state the body more easily recognizes
stored fat for energy as well. Even if that isn't the case, high in fat and protein and low in carbs means that someone on a diet like this usually doesn't have hunger spikes throughout the day.
I personally have found absolutely no problems with exercising
intensely 3-5 days a week, including lifting heavy weights, taking cardio kickboxing classes or doing interval sprints on an elliptical, outside or on a stationary bike