The composition of diamond is carbon, and its appearance looks hard. Both can be bypassed, but the temperature required for combustion is different. So the answer to your question is: Yes.
For jadeite, generally speaking, A goods are not afraid of fire, and B goods will taste when burned. The most typical process of goods B is glue injection, which is epoxy resin and some curing agents. These chemicals are wrapped in jade, so if they are to be burned, it will take a while to smell them. But it is not recommended to use this method to identify the authenticity of jadeite. It will obviously turn yellow. Of course, this fear is relative to not being afraid. If you put him in a steelmaking furnace, you can't keep anything.