Just out of curiosity, I tried to fume some ash with ammonia, and it has virtually no tannins in it. I'd read this prior to trying it, but while I was trying some other pieces, I thought I'd throw some ash in the fumer.
I tried one control piece and one with tannic acid brushed on, and the control piece darkened not a whit. The piece brushed with tannic acid turned a kind of foul brown...not 'xactly what I'd call purdy.