In addition to the possible damage of the turned piece due to moisture, high sugar concentration, etc., I would also be concerned with the distinct possibility of leaching wood extractives into the honey and tainting either the flavor or the food safety of the contents.
I am not sure that tung oil (even if fully "cured") would provide a sufficient barrier to protect either the wood or the honey from one another. I suppose you could line the vessel with a fairly thick impervious layer of food-safe epoxy (or other food-safe film finish), but of course there are issues of wood movement to consider with a fixed-form, inflexible polymerized lining, and the wooden walls of the vessel which are prone to movement due to moisture content fluctuations in humidity, etc.
This sounds like several problems that I'd rather not deal with if it were me thinking about making such a vessel - the glass or porcelain/pottery lining is sounding like a better solution.... or just turn an attractive wooden lid for a suitable vessel and avoid the problem altogether.
Rob Wallace