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