If the turrets can fire in sequence there is a chance.
But if the eagle pilot can fly extremely close to the BS, and fast enough, the pilot of the BS will have serious problems to keep targeting the fighter, Because of the camera speed. And missiles fired from the BS would be unable to lock on the fighter.
(If you find any mistake in my English, please let me know via a PM)
(Really, I speak terrible English, so please, tell me if I make mistakes. I'd like to improve it a bit )