It's probably going to leach tannins for some time yet, possibly the lifetime of the wood (or tank set up).
However, it will probably be pretty heavy at first, and then taper off a bit.
You mentioned that the wood has been soaking in a bucket for about a month, have you been changing the water in the bucket? When I'm soaking driftwood and such, I tend to change out the water when there is a noticeable color change (I don't bother doing it more than 2x a day).
I've never bothered to boil anything myself, but I've heard people claim that it accelerates the leaching process.
I don't think the tannins are necessarily harmful, and that they are often beneficial for many critters. If it caused a rapid pH (or possibly lowered the hardness of the water) swing like you suspect, I imagine that could be harmful.
I'd say go ahead and put it in the tank, maybe put some carbon in the filter, and just keep an eye on your tank - maybe do some water parameter tests and keep a log to see how it's affecting pH, hardness, etc. Do frequent small water changes if you have to.