I'm coming late to this discussion, but I'll put my lab coat on
and throw in my two cents worth.
-Most people say "carbon" when they mean carbonaceous materials. Big difference.
-Elemental carbon has many forms and all of them are difficult to derivatize. Think diamonds and pencil leads (graphite). They sit around unchanged for eons.
-One step up from elemental carbon is carbon with some hydrogen atoms attached to it: gasoline, methane, ethane, buckyballs, for example. Still not very easy for plants or animals to use (note how difficult it has been to find microbes to digest oil from oil spills).
-Wood ash has a lot of stuff in it. Before it has been rinsed many times with water, it is very basic (lye soap is made from wood ashes and grease). Eventually the soluble materials will be washed out and most (but not all) of what is left behind will be compounds with high carbon content but not elemental carbon.
-Activated charcoal is made from wood or bone by heating it at very high temperatures in the presence of steam, air, or carbon monoxide (i.e. a source of oxygen). This process makes it very porous (high surface area). With this high surface area it can adsorb other molecules. It works well for adsorbing organic molecules (molecules containing carbon), but not for inorganic molecules (like water or sodium chloride). Thus it works well to remove poisons derived from organic molecules from one's stomach but wouldn't work well to remove all that salt you swallowed when you ordered the large margaritta.
It seems to me it would remove from the soil things you'd rather have available to organisms in the soil. It will hold on to these molecules for a long time (they won't be available as a nutrient), but on the other hand, you will saturate all the pores pretty quickly, too. At that point, the charcoal is an inert filler. It might help aerate the soil or it might help drainage, but it won't itself hold water in the soil and to the extent it is elemental carbon, organisms (microbes, plants) can't use it either.