I'm from Canada.. Here high vents are typically active, while cold-air returns are typically lower.. When you call that the AC exhaust, you mean thats where the AC comes from right?? Thats not a passive hot air return like what I'd expect to exist in warmer climates.. In anycase, its probably not the best idea.. If its active you won't be able to exhaust when its on, its likely linked with vents around the house, and it may even cause furnace complications that only an HVAC guy could explain.. Any other options? If there is a window you can use that.. Just get some cheap blinds/curtains and put them up, then cover the backside with cardboard, cut a hole in it, use panda plastic to make a diy duct from hole to a fan, preferably angled/bent to keep light in.. (Obviously proper ducting with a proper fan for ducting would be better).. When I used a setup like that I even put a mini tv between the blinds and cardboard, from outside it looked like somebody was living in the room..
That chest should be fine, but if you don't plan to cut holes in it you should keep it cracked with a small fan blowing towards it to keep air in there fresh.. Come curing you'll want jars, but there is no reason you can't put the jars in the chest..