I suppose some absorption would take place but not a great deal (given the one quarter wavelength at 20kHz is a little less than 5mm). Here's the article I referred to above the conclusion of which reads:

As a result, it would appear that the tissue creates the one thing that studio designers around the world try to avoid, fearing it most in their control rooms: Comb Filtering. The paper filters are not absorbing the high frequencies, but simply reflecting them back into the tweeter, thereby causing cancellation through comb filtering.

http://www.bobhodas.com/tissue.html

I'd be inclined to agree with Thorsten (gritted teeth!)