Defense drones take out incoming missiles (and lasers if you have a defense drone II). Do they shoot down the projectiles before or after the game does a dodge check on your ships evasion?
The drone will fire at missiles before your dodge check; there's never a case where a drone will say "Eh, it'll miss, I'll just let it go by."
If there are multiple missiles inbound, the drone will shoot the first, and you will have to hope for a decent dodge roll on the rest.
See also this other question about dodging, if you're thinking about cloaking to dodge a missile that got past your drone.