I haven't placed salt in a box yet, but I would think it shouldn't be a problem.
A box with a good fitting lid is air tight so moisture form the outside shouldn't be able to enter.
Like all boxes, the wood should be dry before finish turning them. Even though there is still some moisture in the wood I'm guessing it shouldn't be a problem. I'm going to have to give this a try.
Imparting flavors can be a concern. I would never make a box from camphor that will be used with food. Having your food taste like Vick's Vapor Rub would be horrible. I've had success with maple, elm, birch and Russian olive. With bubinga, black walnut, and cherry, I kept the lid off for a month or two and when it passed the sniff test I deemed it usable. The bottom line is you need to pick the right wood. Just because aromatic cedar looks nice doesn't mean you should use it with food.
I've also used wax on the inside to seal out the wood's smell. Kiwi clear shoe polish at one time contained Montan wax (harder than carnuba). Lately, I stated using "Turtle Wax Platinum Series Paste Wax" which contains both carnuba and montan wax. Once it passes the sniff test I feel comfortable using it with food.
BTW, I also love to cook.