As a young boy scout of 12 or so, I ate some pork that my patrol and I had cooked over charcoal before all of the lighter fluid had burned off. It tasted like lighter fluid smells. We never made that mistake again.
Pro tip from 12 year-old me: styrofoam cooler lids make great fans to speed the progression of the reaction.
Pro tip 2 from 12 year-old me: don't get the lid too close to the charcoal, or it will melt. Also, wet wool finger mittens can cook and become brittle far from a wet wood fire, because the fire gets very hot when you blow on it to keep it from going out and very cool when you go to check the temperature near your mittens.
I would not cook on burning pressure treated lumber, but the vast majority of lumber in construction is not pressure treated.
Best advice is during hurricane season keep freezer and refrigerator stock to a minimum to keep your losses low. Stock up on non-perishables, but not overstock.
If you absolutely must have cold stuff while the power is out, either get a generator or look into 12V gear.