Agree with the above comments, its all about buffering capacity.
If the alkalinity of your tap water is high (eg 100ppm or above), some drift wood and tannic acid, would probably not drop pH in any significant way.
But if your alkalinity is 20ppm or lower, that'd be a different story.
Or if you have a crushed coral substrate (aragonite) the coral will constantly neutralize the acids,(from the wood and fish urine) just like a high alkalinity does.
When you titrate water to find your alkalinity number, you gradually add a weak acid until the water stops neutralizing the acid. The color changes when it reaches equilibrium, and can no longer buffer the acid that is being added.