Ok, I'm the curious sort, so I did some research on exactly what happens when you use the baking soda/aluminum foil method of removing silver tarnish, and here's what I found:
"When silver tarnishes, it combines with sulfur and forms silver sulfide. Silver sulfide is black. When a thin coating of silver sulfide forms on the surface of silver, it darkens the silver. The silver can be returned to its former luster by removing the silver sulfide coating from the surface.
There are two ways to remove the coating of silver sulfide. One way is to remove the silver sulfide from the surface. The other is to reverse the chemical reaction and turn silver sulfide back into silver. In the first method, some silver is removed in the process of polishing. In the second, the silver remains in place. Polishes that contain an abrasive shine the silver by rubbing off the silver sulfide and some of the silver along with it. Another kind of tarnish remover dissolves the silver sulfide in a liquid. These polishes are used by dipping the silver into the liquid, or by rubbing the liquid on with a cloth and washing it off. These polishes also remove some of the silver.
The tarnish-removal method used in this experiment uses a chemical reaction to convert the silver sulfide back into silver. This does not remove any of the silver. Many metals in addition to silver form compounds with sulfur. Some of them have a greater affinity for sulfur than silver does. Aluminum is such a metal. In this experiment, the silver sulfide reacts with aluminum. In the reaction, sulfur atoms are transferred from silver to aluminum, freeing the silver metal and forming aluminum sulfide. Chemists represent this reaction with a chemical equation.
3 Ag2S + 2 Al -----------> 6 Ag + Al2S3
silver sulfide + aluminum -> silver + aluminum sulfide
The reaction between silver sulfide and aluminum takes place when the two are in contact while they are immersed in a baking soda solution. The reaction is faster when the solution is warm. The solution carries the sulfur from the silver to the aluminum. The aluminum sulfide may adhere to the aluminum foil, or it may form tiny, pale yellow flakes in the bottom of the pan. The silver and aluminum must be in contact with each other, because a small electric current flows between them during the reaction. This type of reaction, which involves an electric current, is called an electrochemical reaction. Reactions of this type are used in batteries to produce electricity."
This is from http://scifun.chem.wisc.edu/homeexpts/TARNISH.html
So, it does indeed chemically reverse the tarnishing reaction, leaving all the silver intact on the piece you are cleaning.