So if the rudder fails or gets stuck in the “left” position a pilot could open the right door and it would essentially counter the effect?
In reality, in a strongly- deflected stuck-rudder situation, the pilot would be best advised to forget about the doors and just land the plane, selecting a runway with a strong crosswind component if at all possible. After all, when landing with a strong crosswind, it's not that uncommon to hold the rudder at close to full deflection in the "downwind" direction. If no crosswind runway is available, the pilot will just have to land the plane going a bit sideways-- no problem if the aircraft happens to have tricycle gear, like most do these days.
Obviously, in a stuck-rudder situation, steering corrections must be accomplished entirely via bank angle changes via the ailerons. Keeping the rate of change of aileron deflection (and bank angle) low will help smooth things out.