Hi Brian, sorry for the delay in responding.
If you’re talking about genuine hardwood charcoal, it’s just wood with no added binders or combustibles. In my opinion it would be fine to use it in your oven once it has been properly cured.
It does strike me that it would be much more expensive than using, say, splits of hickory, cherry, or other popular aromatic hardwoods. The advantage would be quicker lighting and turnup to cooking temperature for grilling foods.
To heat up the entire oven for baking, though, I’d expect you would need an entire bag of the stuff to accomplish what you can do with 6-8 dry splits.
Regular charcoal briquettes are a definite “no”—they are basically sawdust compressed with coal dust and binding agents and they will contaminate your hearth. They are designed for radiant cooking with separation between them and the food (usually a grilling grid).