Does the Corolla 2005 CE allow for the keyless remote locks?

That depends if the car originally was equipped with the receiver for the keyless system. If so, you can buy the remotes from a dealer for about 99 dollars each. If the car does NOT hve the keyless receiver, the remotes will not work. What I would do is take the car to a dealer, their techs can look to see if the receiver isinstalled under the dash.