Yes,it would still survive no matter what.
When this item is held by a Pokémon, if the Pokémon has full HP but is
hit by an attack that would knock it out, this item prevents the
holder from and keeps it fainting t 1HP. The Focus Sash disappears
after use.- Serebii.net
If it has full HP, the holder will endure one potential KO attack, leaving 1 HP.
For more info go here- http://www.serebii.net/itemdex/focussash.shtml
Even if it has Sturdy it will survive with 1HP.
The Pokémon is unaffected by One Hit Knock Out moves and in Generation V, the Pokémon cannot be knocked out when it has full Hit Points
Hope this helps