Well, if you damp them enough so that their resonant behavior and effects on the sound field will be minimized, wouldn't their resonant frequency become kind of irrelevant ?
Or you mean you want to use them both as diffusers and as tuned absorbers ? As far as i know, damping a resonant absorber to the point where it will not introduce reemission in the room anymore will generally make it less efficient for the intended absorbtion job too. So the reemission phenomena has to be used in a constructive way, tunning the device (on both the resonant frequency and Q) under continuous acoustical measuring until you get the best of the room response. But i'm hardly an expert on this part, so maybe others more experienced have better opinions to share on the subject...