Not adding any bittering agent to counterbalance the residual sweetness? Hmm.
Bottling or kegging?
Granted there won't be any antiseptic action that you might get from hops, but if your sanitation is good, I don't see where/why it would "go bad".
It's my understanding that if you just leave it in the secondary once fermentation is complete you should be able to store it for a long time. I have a friend who was just given a 5gal batch of RIS that had been sitting in the secondary for over a year and it only improved. The alchohol content should keep off any I faction providing you don't keep opening the carboy for one reason or another. Just put it in the dark and leave it until your ready for it.
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* Member of the Maniacal Association of Shoreline Home-brewers, CT
If I hit 5-6% ABV, how long will this last before it starts to turn/go bad? Will refridgeration greatly increase the time?
I'd expect 12 months at the most but I could be wrong. Once you've bottled and kept it at room temp for the yeast to carbonate the beer, light & warm temperatures would be the two factors inversely associated with storage longevity. I'm aware higher abv beers do keep longer but I'm not sure about a 5% beer.