Will adding apple cider vinegar to freshly pressed fruit juice preserve it
Apple cider vinegar is commonly used as a food preservative so I'm sure you would see some extended shelf life.  

The acetic acid (the "active ingredient" of vinegar, usually present at around $\pu{5 - 20\%}$) in the vinegar would not "initiate" the production of more vinegar from the juice.  The production of acetic acid comes from a two-step fermentation process. First, alcohol is produced from the sugar in the juice by adding yeast and the appropriate bacteria. Then, acetic acid forming bacteria are added to oxidize the alcohol to acetic acid. 

So, simply adding the apple cider vinegar to your juice will likely increase it's shelf life, but will not result in the production of more vinegar.