Don't want to beat the dead horse too much, but there is no good evidence that materials make any difference to the sound. In terms of flutes, this is a worthwhile study:
http://iwk.mdw.ac.at/Forschung/english/linortner/linortner_e.htm
'Tests with experienced professional flutists and listeners and one model of a flute made by Muramatsu from 7 different materials showed no evidence that the wall material has any appreciable effect on the sound color or dynamic range of the instrument. The common stereotypes used by flutists and flute makers are exposed as “stereotypes”.'
The Uebel aluminum (aluminium) flute is a totally decent instrument....And Galway likes to play one made out of concrete just to show that it sounds fine, too.
Well, perhaps different metals make a smaller impact to the sound than the wood from a woodwind or guitar.
I do believe the type of metal does make a difference, in the higher frequencies and at louder volumes,
it is audible, and recognizable for trained ears and in the studio.
I'm not saying that blindfolded you can hear what kind of material the sax is made of, but if you'd A/B say a copper sax to a nickel one, you will hear some differences.
Any material being exposed to soundwaves on the microscopic plane, do resonate, compress somewhat, bent assymetric, or even deform. Especially saxes.
Many things for the human eye seem impossible, but if you look at a slow motion recording of a golf player hitting a golf ball, or a drummer hitting his snare, you'd be amazed just how much the drumskin or golfball deforms when playing. Something not visible to the eye at normal speeds. (They do have them on youtube those vids).
In a lesser way sound pressure waves do cause a deformation within the instrument, stretching or expanding certain parts of the horn (in places where there is an overpressure of air), and compressing others (pieces within the horn that are near to vacuum)
Even if they did not, just the fact that a sax vibrates as you play through it, and you can feel that, proves that perhaps the walls aren't as neutral (or unaffected) as first thought!
It may be so, that one material would create a much heavier sax than another, even if both materials are as tough as the other. When the sound waves exit the sax's horn, the horn gets pushed back by the back pressure of the sound wave (law of action reaction).
I suppose heavier saxes (eg made by heavier materials or thicker walls) would be less affected by the vibration of the sound waves coming out of the horn (it is only natural to believe that most sound waves get portrayed FORWARD, meaning away from the player, through the horn's bell and valve openings, and that the horn would start being pushed backwards as the soundwave exits the horn. The reverse happens when you'd be at the negative part of the soundwave, the horn actually sucking in air causing it to be thrusted forward.
And an instable instrument, say a sax made of the same material and thickness as a plastic 'throw away' drinking cup, would most likely vibrate enormously at such SPL's, making the quality of the sound less nice, having a less good projection of sound, and that affects the sound quality as well).
So even if the material's strength plays little role in the deformation of the sound (which I do not believe, I think it does make a difference), it's weight could also make the difference in the projection of sound.
Our ears are very sensitive instruments, and soundwaves are very rapid waves. Those waves can be very small, a fraction of a decimeter apart at 340m/s, meaning that a small resonant vibration of the sax could deform the soundwaves at least enough to be audible.