>Inflicts damage equal to the user's remaining HP. User faints. ~ Pokémon DB
If I use, say, Final Gambit Staraptor vs. Focus Sash Breloom, and Breloom has less HP than Staraptor, will Final Gambit OHKO through the Focus Sash?
No, it will not. Final Gambit can still trigger the Target's Focus Sash, Focus Band, Sturdy, or if the target has used Endure, it will endure the hit.
Source: http://bulbapedia.bulbagarden.net/wiki/Final_Gambit_(move)