Yes, plating a gun requires a complete disassembly. About the only thing not generally removed would be something like the old S&W barrel pin or a front sight. All the internals have to come out. In addition, all the old finish has to be removed, plus some parts might need to be fitted so that the gun will still go together and work after a layer of metal is added. It is not just a matter of dunking a gun in a tank, and I strongly recommend using a plating service that specializes in guns. The local "bumper shop" would probably ruin the gun.
Not to be a wiseass but are you sure you want the gun chromed? FWIW, I don't care for chrome plating on guns. It has a cold, rather bluish look that compares unfavorably (in my mind) with the warmer look of nickel plating. I am not sure, but I don't think Colt will do chrome plating.
Jim