DH (general hardness) not enough to detect via test kits, but dKH (carbonate hardness) may well drop some as the carbonates react with the tannic acid that the wood releases.
Fortunately, if you have fish that like acidic water, it won't matter. For the first week or so, test your pH and dKH every day or other day and see what happens. Baking soda is the perfect way to keep dKH in the right range, make sure it's dosed LIGHLTY!!!! It's way cheaper than the "KH buffer" crap sold at pet stores, and those are mostly..guess what.... baking soda.
If you want to get real anal about it you can mix baking soda (sodium bicarbonate) and soda ash (sodium carbonate) in a 3:1 ratio. This will raise dKH 3-5 points per teaspoon per 20 gallons of water. Will also raise pH so be cautious.