Pretty much all yeasts would be comfortable at 6.3%, and honestly most well beyond that point.
The yeast do not die just because fermentation is complete, they just go dormant. And just because you see a giant yeast cake in the bottom, and your beer looks clear, doesn't mean there isn't plenty of yeast in suspension. In fact short of filtration, there isn't much of a way for homebrewers to eliminate enough yeast from the beer to prevent refermentation should you add more sugar.
You could carb it either way. Naturally will add a small but negligible amount of alcohol to the beer.