If you are using a additional containers or surfaces in the oven for baking, you should absolutely pre-heat it with the oven. Use an IR thermometer to measure the actual temperature of the container - a dutch oven or heavy stone will take longer to come up to temperature than the air in the oven will, so the oven will claim to be preheated sooner than it is actually ready.
Remember that temperature and heat are two different things - one of the benefits of using a baking stone or dutch oven or other "heavy" thing is that it stores a lot of HEAT. Air at 450F and Cast Iron at 450F contain very different amounts of heat, and it is heat that will bake your bread. You can tell that they have soaked up as much heat as they can when their temperature is close to your oven set-point, which will take a while.
The only possible exception to this would be if you are just using a thin sheet metal steam tray to cover your pizza stone to trap steam, since it has so little thermal mass. A thin tray could probably be put over the bread without preheating the tray since it won't absorb or store much thermal energy.
To prevent burning, choose containers with a good, solid handle, and get quality oven mitts, preferably with long-ish sleeves to protect your forearms.