I don't know for sure (I'm not into bioactive) but I would think it might kill them, IF, as you said, they actually "break down" (eat?) the wood, as wood is quite porous & will retain some of the chemicals used on it within the fibers.
That's one reason I often caution people NOT to use bleach to disinfect wood furnishings, as the wood will retain the strong bleach fumes that WILL cause harm (irritation & possible more) to whatever creature is stuck breathing it.
With diluted chlorhexidine there's no odor left to indicate it's still there, but I would assume it is- btw, that's what I use to clean my snake's homes & furnishings- and I do periodically use it on branches or wood tunnels- it doesn't even require rinsing as it won't off-gas anything harmful once it's dry (unlike bleach). In cages, I just wipe it dry- no rinsing needed. But with creatures that will dig into the wood, I'd personally error on the side of caution & not use this driftwood with this kind of set-up (bioactive). If you soaked it afterwards in plain water, that might (?) be enough to dilute & remove traces of chlorhexidine from the wood fibers, but I can't be sure.
Sorry, I'm sure that's not the answer you were hoping for but I'm glad you thought more about it- I wouldn't want your creatures harmed.
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