- 2003 study: demonstrated that "the magnitude of the induced wall vibration depends on the material from which the instrument is made and its wall thickness"
- 2005 study: showed that damped trumpet bell audibly affect the sound
- 2007 study: similarly found "big differences" in harmonics in damped bells
- 2009 study: simulation showed that wall vibrations can affect the acoustic impedance, which affects sound
- 2010 study found the same effect on bell damping
- 2013 study: demonstrated that "axial vibrations of the bells of brass wind instruments can lead to audible effects in the sound"
- 2013 study: demonstrates that wall vibrations of the bell affect french horn sound
- 2015 study: found further experimental support for axial vibration of the bell affecting sound for brass wind instruments
My guess is there are more studies that I haven't found yet, but this is enough to show that science is not only open to the idea of wall vibrations affecting the sound of an instrument, but various studies are closely examining the issue and repeatedly finding experimental support for the idea.
As far as this discussion goes for instruments in general, from what I've read it seems like wall vibrations may make a much bigger difference in non-cylindrical instruments, especially when a bell is involved, so instruments like trumpet, french horn, trombone, and yes, saxophone!
Last but not least, for those wondering whether lacquer could affect the sound, from back in 1981 the answer is yes. From the abstract, "the effect of lacquering an instrument, though small, is not musically insignificant."