Will using caffeine as energy to train rather than carbs help fat burning?

I have been drinking sugar free energy drinks mainly rockstar sugar free, to provide energy for training in the gym, in order to minimise my carb intake with the goal of burning fat.

Sessions consist of upper body weights, power sets with high weights and low reps. Every session is finished with 10 minutes on the treadmill at 11 kmph. everyday mon-fri

Evenings can consist of 2-4 hours garden work, BMX all evening, a 3km run or a lazy evening.

This is monday to friday, usually two days BMX, 1 lazy evening, and gardening and running on two nights.

My diet will be most days 1 tinned tuna steak, one bowl of crunchy nut, 2 rockstar sugar frees. 1 pint of nitro-tech shake. Then a meal with salad + quorn or fish, then either potato or rice as the staple carb, occasionally pasta. About 4 days a week I will have a meal, and 2 will be a tin of baked beans, and 1 will be chips from the chip, usually saturday. Weekend breakfast will be a tin of beans, or a large english breakfast. The weekend is usually high contrast to my weekdays in many ways.

cheers Jordan