Yes. All dust covers will affect the sound of a TT in the manner that they receive and transmit airborne vibrations. Left open is probably, and agruably, the worse case scenerio, but i dont think closed is much if any better and closed you have a little echo chamber for your sensitive stylus. I have and recommend removing the lid/dust cover entirely during play. I think this is more a more important issue for unsuspended tables than suspended tables as the suspension assembly would absorb some of these vibrations from an attached cover.
I make this easy by removing the hinges and on the surface of the TT I place small pieces of materiel (of your choice) so that they would touch on the linside corners of the cover. This way the lid is easily removed and replaced when you need to do so, and when in place resists horizontal movement. Now if you've go pets and/or kids who might whack the cover, the recommendation may not be best. But sonically, cover detached is best.
FWIW.
I make this easy by removing the hinges and on the surface of the TT I place small pieces of materiel (of your choice) so that they would touch on the linside corners of the cover. This way the lid is easily removed and replaced when you need to do so, and when in place resists horizontal movement. Now if you've go pets and/or kids who might whack the cover, the recommendation may not be best. But sonically, cover detached is best.
FWIW.