I don’t really see how there could be many benefits to drinking pickle juice. I mean, anything is possible, I just haven’t heard about this yet. I suppose it could help in maintaining adequate sodium levels, and possibly have some beneficial bacteria depending on if the pickles were fermented or not, but otherwise there isn’t much nutritional value in drinking pickle juice.
The biggest issue I find is that pickle juice is typically loaded with preservatives, as are all pickled products (otherwise they’d go bad or start to ferment). Most preservatives have a negative impact on our bodies, so I’d probably recommend avoiding them. I like a sip of pickle juice as a treat here and there, but I wouldn’t drink glasses of the stuff on a daily basis.