likely not. alcohol is produced by yeasts who convert sugars to alcohol. pickle brine has likely too little fermentable sugars and a too low pH. so unless you dilute the brine heavily and then add more sugars (and most likely extra nutrients) nothing is going to happen.
But: you could make a sort of vegetable wine https://homestead-and-survival.com/16-best-fruit-herb-and-vegetable-wine-recipes/ and a) don't wash your hands or leave it uncovered during fermentation (you will get acetic acid producing bacteria) or b) at some point during fermentation just add enough pickle brine to stop the fermentation.
but why on earth would you want to do this?
if it's the vinegar you are after just make a shrub https://en.m.wikipedia.org/wiki/Shrub_(drink) and add some spirits of you choice
I bet the yeast will struggle with the vinegar and salts, which act as a preservative. You could make alcohol from non-pickled cucumbers but you'll probably need to make a mash from a whole lot of them, as they do not contain much sugar
Pickles, sauerkraut, and similar are fermented through bacteria, that produce lactic acid. For alcohol you'd need yeast instead. As such, I don't think that you can use pickles to make alcohol.
Pickles aren't necessarily fermented. In fact, I don't think I've ever done across a fermented pickle, and my partner and I try any new pickles we find
I'm aware of vinegar pickles (I've eaten and prepared both), but those would be even worse for booze production.
I've had this notion that pickling is what you get when fermentation fails? This is not based on any background in chemistry, but rather my experience in trying a friend's homemade wine and noticing its vinegar undertones. Keep trying, man, you'll get there!
Pretty much no.
There might be a way to process the pickles into having enough sugar/starch to turn into some amount of alcohol, but I kinda doubt it would work well.
Cukes aren't exactly going to make much alcohol before they're pickled, not without added sugar to the degree that you're actually making the booze from the added sugar rather than the cukes. Cucumber wine does exist though. Some people like it, and I've heard that it has been distilled into something resembling a liquor. But, again, the amount of sugar added to get enough alcohol to call it wine is enough that the cucumber is more of a flavoring than the actual fermented product.
You'd need to rinse and soak the pickles for at least a day, change the water and do it again. You gotta pull out as much salt as possible. That would be after slicing them into fairly thick pieces. If you don't get enough salt out, the yeast can't do their job.
After that, you'll be left with pretty much tasteless plant matter, but it should be able to be pureed and used as a base for the yeast. You'll need to add probably half the weight of the now pulped pickles in sugar. Maybe even 3/4 the weight since you've also lost some of the sugars in the original cukes.
Add your yeast, keep it safe, and wait a week or so. Strain the resulting liquid, then put it back into a container and let it sit for another week or so. Some "wines" produced this way take only a few days in this step to have enough alcohol to taste, but cukes take longer, so I have no idea how long you'd need to go for pickles, what with the residual salt slowing the yeast.
IMO, you'd be better off making pickle infused booze, or just mixing some pickle juice into your booze (which is a thing already, though I can't recall the names of the cocktails, it's been way too long since I was around bars and bartenders).
