Almost every jar of pickles claims a serving of pickles has zero calories. Now clearly, this is incorrect and the result of exploiting some ridiculous FDA loophole, since anyone knows that cucumbers provide calories.
So let's say you're in a situation where you lose all access to food, but you've got effectively unlimited access to pickles -- like, you're trapped inside a recently abandoned pickle warehouse.
Could you conceivably eat enough pickles to survive for a month? Two months? Or would your body just shut down from all the sodium and acid?
I'd give it 3 or 4 days, if literally all you have is pickles. All that salt and vinegar will dehydrate you pretty damn good, despite all the liquid you're ostensibly consuming.
Even if you had fresh water present as well, I think you'd wind up with one hell of a stomachache by day 2 or 3.