If the damage from disintegrate reduces a half-orc to 0 hit points, can Relentless Endurance prevent the orc from turning to ash?

Yes. The disintegrate spell turns you into dust only if the spell’s damage leaves you with 0 hit points. If you’re a half-orc, Relentless Endurance can turn the 0 into a 1 before the spell can disintegrate you.