Anything you add to a drum will change the sound. I doubt that the acoustic qualities would be noticed that easily... especially when you have the drums buried in the mix. I'd focus that attention on just tuning the drums. It sounds as if they are either talking from you know, back there, or they have nice enough equipment to make a difference in picking up such small details.
But you do raise a point. Finish does impact the drums overall sound... however small/large that might be. If you have a oil/stain type of finish it will soak into the wood... then however much lacquer you have over that will decide how much the drums tone gets muted. If you have say a wrap on the drum it will muffle the resonance of the drum more. Here is the tricky part though... if you have smaller shells you will get less resonance from the drum in the overall sound.
It works out to being pick your poison... but I believe that the impact is very minute.
This goes a little more in depth...
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