Disclaimer: this is purposefully obtuse.
Other effects in the game which explicitly state they kill you:
Shadows, succubi, massive damage, death saving throws, beholder death ray (notably not even their disintegration ray kills you), power word kill, vampires, mind flayers, night hags, drow inquisitors.
Clearly, if they intended for disintegration to kill you, they’d have said so. Since specific overrides general, and there is no general rule that disintegrated creatures are dead, I rest my case. QED.
I see no flaw in this argument. Instead of dying, the character exists like the guy from “One” by Metallica, desperately waiting for a stiff breeze to end his existence.
Dust pan, imprisoning me, all I can be, a pile of fine dust
I cannot live, I cannot die, turned into dust, scattered across the floor