The better Japanese turntables have dustcovers made from 5 mm thick (a few are even thicker!) acrylic. They are probably not going to transmit resonances, as pacific stereo said --at least, not in the higher frequencies. However, there are still some issues.
In the down position, they can --because they are essentially large, hollow boxes with stiff sides-- act somewhat like resonators, at least at some frequencies. Think of drums. Think of string instruments. Think of how hollow-box style plinths compare to solidly-filled plinths. You are still putting a big, potentially resonant box over your table, probably not a good idea. How they are mounted --the hinge and bumpers-- might also make a difference, in helping to reduce the transmission of vibrations into the plinth, but it won't stop any air transmission under/inside the DC.
What about putting them up? In this position, they will act like a horn or ear trumpet, somewhat like those "Big Ear" listening devices, to reflect sound waves down towards the platter, record and (possibly microphonic) stylus and cartridge. Also not a good idea.
Ever notice how almost all dustcover hinges have a simple, easy way to remove and replace the dust cover (just slide it over and lift it off)? Why do that if the cover wasn't made to be removed? I think every mid-fi and high-end TT I've seen has this; only the very cheapest ones don't. That is, if they have a dust cover at all; some of the very high-end "exotic" tables don't have dust covers at all! I think this tells us something about what manufacturers think of dust covers.
What about dust? Realistically, how much dust will fall on a record as it is playing, during the time it takes to play it? Unless you live outdoors in the Gobi desert, it's a very minor consideration, weighed against the negative sonic effects of having the DC on.
With all these things weighing against them, I choose to take the prudent course and remove the DC when actually playing records, even if the DC is a heavy (5 mm) one. The rest of the time, I keep the DCs on, to protect the turntable from dust, as intended.
In fact, I go one step further with my best turntables when they are in sunlight and put clean, soft cloth over them, to help protect them --not just from dust and scratching (even just from wiping dust off!) --but from potential UV degradation due to sunlight. I got the idea from the old man who kept his (=now my) PL-C590 under a towel (when not in use) its entire life. After a couple decades, it still looked brand new!
All this said, I think a separate box, well-damped and insulated against sound, that completely covers the TT and its plinth/base, would IMPROVE sound. No more microphonic effects from the speaker sound affecting the pickup. But then --unless you made it from blown glass with a vacuum sucked out between them-- you wouldn't be able to see the records playing, and where's the fun in that?
Hhhhmmm, you COULD make a cabinet fairly easily with sides of pre-made double-paned vacuum glass (made for windows), with thinner wooden frame, using a beautiful wood that complements the TT base, with nicely-molded edges, and good sealants for where the panes are set in, to cover the whole TT and better isolate it from the environment. Might look good, and might work to improve sound. In fact, come to think of it, how about operating a TT inside of a vacuum? How would that affect sound, and what adjustments might have to be made? A nice DIY experiment... for my retirement!
