When they perform a root canal, is there any of the silver amalgam filling placed in the tooth?

Yes, after a RCT. After a root canal therapy (RCT) has been completed, it will require some type of permanent dental restoration. There are two basic options that you have for restoring an endodontically treated tooth: 1. the placement of a dental crown or 2. A filling silver amalgam or tooth-colored composite).
Some do, I do not. The root canal filling material is composed of gutta percha. It's actually the orange wound rubber stuff inside of golf balls to give them compressive strength. Prior to an eventual finishing crown, some dentists will use amalgam fillings to restore the bulk of the tooth on top of the root canal. I prefer to use a a carbon-fiber reinforced post as a rebar inside of a composite filling instead.