The book for you is
Sally Fallon's Nourishing Traditions. In there, she talks about how to ferment commercially prepaired foods, how the different commercial preservatives effect a ferment, and generally ways to increase nutritional value in our Western Diet. I don't have the book in front of me, but I remember an interesting bit about adding active ferment juice (sauerkraut or whey I think) to a can of beans, leaving it room temp overnight, and the live culture activates all sorts of the dead nutrition. I haven't tried this myself as I don't trust commercially prepaired food
enough to leave it open on the counter with or without a live culture in it. But the general theme is that if anyone can tell you how to ferment commercially prepaired pickles, then
Sally Fallon is your gal.
One idea that Sally Fallon and a lot of writers since her use, is to add whey or live culture sauerkraut juice to a food just before serving it. So, if you have a bowl of soup, you heat it up, add a splash of sauerkraut juice to it, then chow down, the live cultures in the sauerkraut will activate things in your digestion that allow you to absorb more of the nutrition than you would have otherwise.
What I say next is a bit of interpretation from reading and personal experience. Keep in mind, I'm just anther person on the internet who claims to have healed herself from a life threatening ailment by using food as medicine. For a much more credible source, I highly recomend Katz's Wild Fermentation or for a more in depth take on the subject, Katz's extremely thick Art of Fermentation.
My understanding of fermentation is that it makes food more nourishing to us in two different ways. First way is to pre-digest the food so that it's broken down into simple to use parts for our body. The other way is that the live cultures (the probiotics) activate mechanisms in our body that help it absorb more nutrition than it would otherwise.
When we cook food, we've already broken down the raw ingredients, albeit differently than when we ferment food. We've also killed most or all of the live cultures that naturally occur in the food. There are very few traditional fermentation that start with cooked food, and most of them utilize a yeast or mold based ferment (like beer or miso). Bacteria based ferments, like sauerkraut or other fermented pickles, often start with
raw food or with foods that haven't been heated enough to pasteurize them.
This of course is generally speaking - there are exceptions.
Processed pickles (generally) have been pasteurized with heat, chemicals or more often both. The veg have also had their basic starting blocks changed a bit - by being cooked during processing, or by exposure to acid, what nots. So your basic live culture sauerkraut juice may or may not have anything to work with in the pickles.
But it will help your body absorb more nutrition.
In other words:
It's worth a try to ferment commercially prepaired pickles. It may work with some brands and not with others. Depending on how the pickles were prepaired it may help, it may do nothing, or it might not take and allow something unpleasant to grow in it. It's worth a try, but a cautious one. As usual with food you make yourself, trust your instincts and your senses as your primary guide to safety.
If you do go the fermentation route, please let us know your results.
Another option is simply adding the live culture juice at the time of eating. This may be enough to give you the nutritional boost you seek.