I may not be a good source on the subject because my working methodes is so that I add the varnsih before I start to monitor the modes of the plates. The thciknesses will also be unaturally thick prior to varnishing.
In my master thesis work I monitored the modes in some violins and a white hardanger with rather thick plates (as usual prior to varnish for me) + two unconventionally built violins. The Q values of the modes was recorded by a rather cumbersome manual process, but they are given in Figure 8 in this article for the modes seen from the top plate side.
http://home.online.no/~an-buen/Buen_article_smac03.pdf If you compare the diamond shaped values with those from the varnished fiddles you see that there is not really much of a difference. But here the fiddles rested on a cushion of rubber foam (stood upright on that foam) and against a rubber grip in the neck, se illustration in the article. I think that mounting may have added some damping to the modes. Using optic methodes like TV-holography requires the object to stand at rest. Suspension in rubber bands would have been impossible because the fiddles would move too much.. (With system using a pulsed laser you can hold the object in your hand and the stability is not so important. The stroboscope effect makes the object be enough at rest. We used a continuous laser).
I am now doing modal analysis using George Stoppanis software which does mode fitting as a part of the procedure. Then the damping factors come out as one of the fitted parameters in a table. So its easier to do this kind of analysis now. I have just started doing this and only on varnisned instruments this far.
George Bissinger has written articles on damping too. My stand is that varnish and sealer does damp the fiddle a little, but as long as the sealer and varnish is dry and the thickness not excessive, the effect will be small on the tone. Holding for playing will have a comparatively larger effect.
I think the moisture content of the wood may play a role for damping and that much used instruments may be more damped than drier ones. Moisture from sweat and breath adding to that effect. Microcracks may also have a damping effect, and may even be nonlinear so that the effect is small at low levels, but much stronger at higher levels. But much of this is speculation.
I have heard at least one maker say that he had stripped a fiddle due to data he got from a modal analysis. I think he had changed his varnish system. But again, the modal analysis is usually done with the fiddle hanging in rubber bands with small loss effects comapred to what you get holding it for playing..
"The only real valuable thing is intuition". Albert Einstein