You can quantify the difference by making a high-bit recording of your turntable without the speakers playing, and with speakers playing at your customary listening levels, and compare the two files. If you put the two files through a program such as DiffMaker by LIberty Instruments, it is possible to extract the difference component and listen to it as a distinct "distortion" track.
Not sure why you would want to do this?
Listening through a fine set of headphones with a great amp will remove all the room effects, the equipment positioning effects, the 'supposed' air-borne feedback effects as well as all conjectural problems regarding speakers.
When I listen through the Audeze LCD2 headphones through the Schiit Lyr headphone amp I hear no reduction in distortions compared to my speaker/room/equipment interface.Rather, through my speakers/room/equipment interface I hear exactly the same spectrum of sound quality as through the headphones with an added air, transparency, depth, bass impact, instrument positioning and emotional content.
There are no theoretical arguments which can turn 'black' into 'white'.
I don't doubt the experiences of others.......I expect the same respect for mine. :^)