Is the chalice an item you bought somewhere, or are you doing some cleaning on a chalice that is still being used in sacred liturgy?
That might make a difference, speaking strictly in ecclesiastic terms, as to how you would treat such an object.
But in either case, I don’t know why you would want to not dry the chalice thoroughly. Water is notorious for leaving spots on any metal (think of chrome on your car after a rainfall,) and if you live in an area where you have very hard water, the mineral content of the water drops may start the process of corrosion on the metal. Even stainless steel will get spots on it.
If your chalice is lined with yellow metal, it is probably gold plate. Gold can react with the chlorine in your tap water.
For any precious metal, I would wash it gently in warm soapy water, rinse thoroughly, and dry thoroughly with a lint-free cloth. If you are not going to use the chalice for drinking purposes, I would also apply a light coat of a metal polish and buff it to a high shine to protect the metal.