First, no. Simply because the word immunity does not apply to energy drinks. Energetics is not a contagious disease or even a foreign substance in the body. Well, no more alien than any food.
Second, energy drinks can theoretically develop tolerance . More precisely, not to drinks as such, but to caffeine, which is actually the main active ingredient in them. And this tolerance may not affect everything, but only some of the effects of caffeine - and it besides invigorates and makes the heart beat faster, and even a diuretic in addition.
And therefore the most useful question in this case is this "theoretically" - is it like in real life, does it happen or not? And as far as I know, the correct answer is and the hell knows .
There is a lot of anecdotal evidence (I'm not sure how it is in Russian, "life stories" or something) about people who drank and drank coffee and he stopped invigorating. There are studies that show that it does not stop, but in rats. There are the same stories from life from people who drink coffee in buckets, but it invigorates all the same - like me, for example. There are studies in which tolerance develops and in which it does not. There is "it is logical to assume that if you drink some of the energy, then they will stop working" and there is "it is logical to assume that the Earth is flat" - because life in general and neurophysiology in particular are full of completely unobvious and unintuitive "but the hell is there."
In general, you can find as many confirmations for any possible point of view as you like, but no one can give an unambiguously correct answer to this question yet.
I have not used energy drinks before, that is, my addiction could not develop. But using them now, I do not feel the expected effect; rather, on the contrary, I become lethargic and fall asleep. Perhaps this is due to individual sensitivity to caffeine.
About "immunity". If you use energy drinks for a long time, you will develop an addiction, but you will not feel a surge of vivacity, and you will drink them simply because you are used to it. Your heart and pancreas will definitely not be happy, and your immune system will most likely work against you.