Yes. Personally I have never added salt to the mixture, because baking soda already contains sodium, but this is the procedure I have used with success on simple silver pieces or a coil of wire: line a glass baking dish with aluminum foil; place your sterling silver wire coil or jewelry pieces on the foil and cover it with a thin sprinkling of baking soda; add boiling hot water to cover the wire or jewelry; use a wooden chopstick or other non-metal utensil to gently stir the items around a bit so they all have contact with the aluminum foil at one time or another. When satisfied, remove the items and rinse thoroughly under tepid running water, and pat items dry.
For more stubborn tarnish you can also assist the cleaning process by using a soft toothbrush during the rinse process.
Please be aware of not using this method to clean pieces that contain pearls, soft stones that have not been polished professionally like turquoise, and never add ivory, opals, or any precious stone that may have enhancements or treatments such as wax or oils that are often used on sapphires, rubies, and emeralds!
On those pieces, I just use an ionic cleaner such as the Speed Brite, which can be used safely on everything except ivory.