Obviously, that ended up unresolved (since for every hippie website that says that it's the nectar of the gods, there's a breadhead website that points out folks killing themselves from over-vinegaring), but it led to talking about kombucha, which led to my considering the idea of apple cider kombucha.
I'd toyed with a peach kombucha (by way of a tea with dried peach bits in it) and a raspberry-blueberry kombucha (by way of boiling the heck out of said aforementioned berries and tossing them into the initial tea mix), but not with just plain juice. In doing a bit of checking concerning the sugar content of your standard apple cider, it seems that it has about 416 grams of sugar per gallon. The way I currently make kombucha, it only has around 200 grams of sugar (IE: a cup of standard 'table sugar') per gallon, so that should actually work quite dandilly!
I'll probably try it with straight apple cider (boiled to heck and back first, so there aren't any wild yeasts creeping in) initially, with some teabags steeped in the cider, and then see if it turns out too sweet -- if so, I can just water down the cider.