Here is way more info on bottle conditioning than I think anyone might need!In regard to refermentation with fruit, I do not think that goes hand in hand with bottling at Jester King. Otherwise I think you'd get crazy amounts of pulp in the finished product. Another thing is that fruit fermentation varies wildly and you'd get big variation from bottle to bottle and batch to batch if it were used to prime/carbonate the beer. Who knows though, they have a lab so they may be able to account for it and use the fruit to prime/carbonate the bottles.
In the page I just linked, there's more info on the sugar involved. Priming with sugar doesn't really impact the flavor of the beer much at all, as you're using a neutral sugar that gets eaten away by leftover yeast. If you prime with the correct amount of sugar/yeast left in the beer, then you should end with a great carbonation level and pour.
To make it more wine related, disgorgement with sparkling wine is the method used to remove similar byproduct from the wine (dead yeast and leftover items from aging). This helps clear it up and uses gravity/vibrations to filter the wine, whether through old school hand riddling way or with machinery.