Could a calorie-free energy drink help losing weight, when used in combination with exercising?

It's a bit of an illusion. Energy drinks are full of stimulants and many stimulants are diuretics (they make you pee more) which makes it look like you're losing weight because you have less water in your system. Also, not having a good water balance is a bad idea when exercising (which is when you need more water than normal, not less).

Calorie-free drinks that don't contain stimulants are fine, though, as they are mostly water anyway and the additional ingredients don't really affect you much. Personally, I prefer just plain water, though.