I'm planning on doing lots of burning of trees cut down last year also. I am thinking(hoping) is will raise the alkalinity level some, but I know not the hardness, as it washes in. I dont think it will have a detrimental affect. I have put in 5 tons lime in and around 1/2 acre, and still have only about 20ppm hardness. Lots of pines, you know.
I think too much N2 is usually the culprit, and raising alkalinity allows it to be released, so it should have a similar effect as lime.