Yes, some studies have shown energy drinks can improve your focus, which helps with studying.
Caffeine is the main ingredient that helps with focus and concentration - it stimulates your nervous system, giving you a short boost of energy, which may also increase your mental clarity/focus.
However, not all energy drinks were created equal. For example, trying to down a Full Throttle - one of the most unhealthy energy drinks out there - may do more harm than good. Since it's loaded with sugar, it'll end up dehydrating you.
Your mind needs plenty of hydration to focus, so dehydrating yourself is definitely counterproductive in any situation, but especially when studying.
On top of that, an energy drink like Full Throttle or Monster will likely give you a short-term energy boost followed by a crash soon after, not ideal for studying all night long. You might be productive for the first hour or two (tops) but then you'll crash faster than a race car slamming into a wall.
You ought to choose your energy drink wisely for studying - a supplement that not only boosts energy and mental clarity, but hydrates you as well, and sustains that feeling for a long time, rather than making you crash shortly after peaking.
Lastly, there is no substitute for a good night's sleep and proper nutrition. Taking care of your body is of the utmost importance, not only for focus during a study session but elsewhere as well. Your body is the vehicle for your soul/mind, so treat it well.
Waking up hungover after downing 10 shots, eating a Big Mac, fries, and a shake, then pounding an energy drink for an all-nighter study session is NOT a good idea.
But assuming you've had a good night's sleep, exercise, and eat right, the right energy drink can be a student's best friend during a late-night (or early morning) study session.
By the way, if you'd prefer to study in the morning rather than staying up all night again, check out our post about studying in the morning without feeling sleepy.