Yes, but make sure you get the new one and the correct model if you go that route. Noblex makes Docter, and only some of them are rated for the back and forth hammering of life on a short recoil pistol slide (ask me how I learned that). It looks like you have a milled slide, which for a regular P226 means that you can just have the slide milled to accept it. Mine is an X-5, so it has an internal extractor like a 1911 which doesn't leave enough material to mill the slide for an RDS.
If you're going to have to tear it completely down to get all of the metal shavings out, another thought is that you could get Gray guns involved. They're the best at Sigs, and did most of the custom work on the internals of my gun (though any competent smith can work on a 226, and the only real reason to send it to Gray is that they can put a nickel/ceramic coating on the internals that prevents corrosion and makes cleaning easier at the same time).
Anyway, nice work on saving the gun, and please keep us posted as to where the project leads you!