This is completely dependent on other factors. Weight loss is dependent on a hell of a lot of things in tandem. It is mathematically strictly better to say, drink only black coffee or sugar-free energy drinks in the morning. Caffeine is an appetite suppressant. The difference is that most people don't have the personal willpower to stick to the fasting without a few calories to help them along.
Weight loss in general is precisely mathematical in pacing and it will absolutely make you lose weight faster if you consume less calories.