I'll assume the sea salt us for the heat-proof base. The answer is yes: you could. People will also use sand or powdery ash.
As far as just wrapping some dried herbs in paper and lighting it, that's where I'd have to shy away a bit.
Incense is so aromatic because it smolders. What you described sounds like you may just ignite it and burn it. If there is a flame, it is burning.
Also about the paper: If you do make some set-up so it smolders, that is there is a self-sustaining ember but no actual flame, then you would get a lot of odor from the burning paper. It is why incense is either made such that it sustains its own ember -- such as the common stick or cone incense, or self-sustaining powders -- or a small amount is added atop a lit coal. Charcoal will have very little odor of its own.
Be careful with the disc-shaped self-lighting discs, however. They light by means of a chemical reaction; beware inhaling much of the smoke from that. And yes: That part will stink a little. But it will settle down a lot after.
Regular charcoal for a barbecue will not sustain an ember very well; it is too dense. It works better in a heap with other coals, as a larger mass of heat with decent enough airflow to continue combustion.
And some people do prefer bamboo charcoal, as it can be lit with just a flame (maybe a candle -- I have never used it), and does not use harsh chemicals. However, it can be expensive.