Here's something useful. There were some people who have tried this at basicbrewing.com search for base malt experiments and you will find three videos in which they attempted unhopped "beers" in 2008. Out of three trials, two, using dry yeast, did become sour during fermentation, however one was not. And the one that was not, was said to be drinkable, but somewhat yeasty due to the yeast character, if I heard them correctly. It was also tepid since it was not chilled.
So yes, it's possible, it's drinkable, you're going to have to be very careful with it, and yes it'd be prone to becoming sour. Even if it's fine out of fermentation, I would expect that room temperature storage is not a good idea, and that leaving it as such (with any exposure due to ..anything really...) will expose it to souring elements and as such, would need to be preserved in the cold, and not left at room temperature to age, like we would do for normally hopped beers.
My stance was and still is, that assuming that there is no contamination during intial brewing, that refridgeration will preserve an unhopped beer compared to no refridgeration, and yes, I completely agreed and still agree that it is more likely to sour sooner than hopped beer. How soon at refridgeration temperature is the question I was wondering about, but again, I get mentally side tracked, hmm... would flash pasturization do anything in a commercialized setting to this style. But the more important question is how does it taste?
From personal experience with a higher % beverage, I know my unhopped, unpasturized sake will last for a few months in the fridge and is still good, but that will not last for a weekend outside the fridge. At least it was only a half gallon bottle that I forgot to store away, the lactobacillus really went to town on it.
ooohhhh, that reminds me, I still have two bottles left in there that I really should finish up... that's going on 4-5 months now... (And they tasted fine two weeks ago when I was actually bottling the things to put into smaller containers).