Wood Ash in the Compost works GREAT

[toxcrusadr]

Unless the fire is extremely inefficient, ash is mostly minerals rather than carbon. There will be charcoal bits of course, I get them even in ash from my very efficient woodstove. But if we're talking "ash" not charcoal, it's mainly oxides, carbonates and silicates of Ca, Mg, Fe, K, P and a host of trace minerals.

Composting definitely takes the pH toward neutral. I don't know how much ash you'd have to add to overwhelm that effect and end up with alkaline compost. Then you'd have to factor in leaching if the pile is not covered.

Ideally, we should all be leaching out the alkali materials to make soap, and then the ashes are neutral, so right back into the soil!