Drug use in military operations actually isn't very exotic. As one can glean from this (I can only assume "woefully") incomplete list on Wikipedia, stimulants like cocaine and amphetamine are, or have recently been, used by armies around the world to keep soldiers awake and alert. In addition to this, the "Short but Sobering History of Drug Use in Wartime" mentions alcohol, opium, cannabis, mushrooms, and more.
Generally, if Drow aren't too concerned about ethics or long-term performance (or are willing to waive these concerns for the Wild Hunt specifically), there's a wealth of performance-enhancing substances other than stimulants they can employ which have all sorts of nasty side-effects which can serve your narrative. For example, anabolic steroids (synthetic testosterone, basically) makes your body build muscles faster; as a side effect, it also tends to turn users into violent psychopaths, which might be desirable during the Hunt. (And in Drow society in general, perhaps?)
Throw amphetamine-like drugs and something like steroids together and you have a bunch of hyper-speeded, strong, and violent psychopaths, but they need some fun!! too, right? MDMA induces euphoria and so it seems like a good start, except that it also increases empathy, but on the other hand, you never know what happens when you start mixing drugs - or perhaps Drow have managed to get rid of that highly undesirable property from it. (On the third hand, it would be kind of interesting if some of the Hunters did end up soft-hearted, feeling sorry for their victims and whatnot.)
Now, the above mix of psychoactives could perhaps be a little bit volatile, especially since the way drugs affect users depends on a lot of variables (and I'd guess the drugs wouldn't exactly be administered in an orderly fashion). The Drow realize this, so they bring extras of all their drugs, just in case they'd take too little of something, or if the effects wear off. But since this is pretty serious business, they don't want to take too much of anything... or rather, they want to be able to fix it if they do. So they bring even more drugs to counteract their other drugs, for example depressants to counteract the stimulants. Feeling shaky from all the uppers? Roll a fat one, have a smoke, calm down for a bit, and you're ready to Hunt again! This practice will obviously cause individual performance to fluctuate during the Hunt, but hopefully there's always someone in a "good" phase, ready to make sure their Hunting buddies don't derail things too much.
This might sound like a lot of preparations - because it is - so they've earned a few pints. And after all, Hunting is thirsty work!
During the Hunt, Hunters are partitioned into groups which operate independently. Upon conclusion of the Hunt, some groups won't return as they've faced disaster (more often than not of their own making), but with groups being independent, those disasters won't propagate affect other groups. (They are also deployed at different locations so if someone for example goes haywire and triggers a volcanic eruption or something, not too many other groups will be affected!)
Most groups do return, though, many enough to call it a success. The skilled (and/or just plain lucky) Hunters are celebrated by the people; the failed Hunters are at best forgotten, but more commonly have their memory dishonored. Although there are some (fortunately very few!) killjoys who propose banning, or at least moderating, drug use during the Hunt... that would really bring down morale, and we can't have that, can we?