burgermeister,
I'll take a shot at it...not scientific, however.
In our soils in East Texas we are generally deficient on Potash anyway and at worst you will be adding that to your system, which seems to me to be a good thing.
On the other hand, tallow trees are toxic to humans, even the smoke from them, so be careful. Just to be safe I don't think I would burn tallow trees in my drainage system and certainly not stand downwind from the burning.
