Despite the fact that the 200 Flying Rats gets the player an Annihilator, the helicopter hardly ever spawns. If someone uses the window cleaning platform, and has a better chance of it spawning by using a helicopter to reach the top, which is extremely illogical, unless the player is using another kind of helicopter and wants to use the Annihilator. There are other spawn points for the Annihilator which are easily accessible without the need to kill the Flying Rats, effectively rendering the helicopter as a reward useless.
"Flying rat" is a New York slang term for a pigeon.
If you are struggling with finding all the pigeons, try hunting at night. The low lighting provided by night makes the orange glow given off by the birds much more noticeable.