It works.
Cloyster used Icicle Spear!
It's not very effective... The foe's Aron held on thanks to Sturdy!
The foe's Aron lost 92% of its health!
It's not very effective... Aron held on using its Focus Band! (placeholder)
The foe's Aron lost 0% of its health!
It's not very effective... The foe's Aron lost 8% of its health!
Hit 3 time(s)!
Source: I believe that you ad I have tested this, LeBoss.
Take a look:
>There is a 10% chance that when the holder is hit by an attack that would otherwise cause fainting, it can survive with 1 HP. Can also protect against multi-strike moves, recoil damage, self-inflicted confusion damage, and damage from Future Sight or Doom Desire.
Even if it had Sturdy, it will still protect, no matter what.
Source