I LOLed
To give a slightly more serious answer…
Pickling only works when the amount of acid/salt/sugar is relatively high compared to the product being pickled. When you’re sticking a cucumber in a jar of water, there is a lot of acid/salt/sugar. The cucumber dilutes that out somewhat, but there just isn’t enough water in the cucumber to make a significant difference. People who re-use pickling liquid always add a little extra vinegar or salt to make sure they don’t over-dilute.
Because there’s not a cup of acidic liquid in the typical vagina, the water content of the cucumber would be really quite significant. It’d be like doing your pickling in a teaspoon of vinegar. The cucumber’s moisture would more or less neutralize the tiny amount of acid, and its sugars would make it a playground for yeast and/or bacteria.
I’m still looking for my horse and cart.
Pain, suffering, and interestingly colored discharge.
I would think it would work if a person is a real sourpuss.
flees
Una better run while she still can.
Patty Piper packed a peck of pickled Peters…
There’s not a cup of liquid, but it keeps getting generated. Plus, we could use a very small cucumber.
Uh huh… Just promise me you won’t tell me how that turns out. 
You know what they say: “It’s not the size of the cucumber . . . .”
According to a brief look at the internet, cucumbers are best pickled at temperatures in the 70-75 degree range, and vaginas tend to be considerably warmer than that, so I imagine that could interfere with the pickling process. And since the body tends to basically shut down at body temperatures considerably higher than 75 degrees, I imagine if you had a vagina at that temperature, it would not be producing the typical secretions.
Maybe if she’s Jewish?
I don’t know the answer to the OP’s question. The closest I’ve personally seen is a vagina shooting a banana across the room. It did not seem pickled.
But were you pickled?
Maybe there’s spooky pickling-at-a-distance going on here!
I’d rather not say.