Yes, it is possible for bacteria to grow in pickle juice. In fact, several studies have shown that the lactic acid present in pickle juice can be a conducive environment for certain microbes to thrive.
One study conducted by researchers at the University of Arkansas examined different brined foods including pickles and found that Lactobacillus was the most common type of bacteria growing in the samples. Researchers hypothesised that this might be because lactic acid is generally present in high concentrations due to fermentation processes used during food preservation. The growth of other kinds of pathogens such as Salmonella and E. coli have also been documented when contaminated ingredients are added too early or under unsuitable conditions during preparation or storage of foods preserved with acidic solutions such as vinegar-based brines like pickles made from cucumbers and other vegetables.
In conclusion, while there may not be any significant risk associated with consuming typical store-bought dill pickles, it's always important to follow proper safety guidelines when making your own batch at home—including refrigerating them instead of leaving on the countertop—and throw away any jars if you suspect they’ve gone bad.