It is the wood gasses that create the high heat and efficiency in an RMH, the char would already have all the combustion gasses used up so I don't think it would work.
Charcoal is the proper fuel for forges, grills and smokers. This is because it will burn at high temp with the addition of air, which is necessary for heating steel or iron to workable temperatures.
A good working rocket stove actually has a double burn; the wood burns and releases the gasses which get a second shot of air and burn from that (think of a rocket stove as a jet engine with an afterburner)
There are also batch stoves ( a rocket stove idea but one that doesn't need fuel added as it burns. batch stove gives all the particulars you should need.