Yes, that's right.
It works as cool compress. Put a spoon in the refrigerator for some time until it is cold and freezed. Then take it out and apply to your eyes. Don't forget to close your eye when you put the spoon on it. Keep the spoon on your eye for about 10 minutes. When you finish, repeat all these steps to the other eye.
Well, looks like you are very worried about the situation you have. True, dark circles would definitely damage our looks. But shall I remind you that a metal spoon could only relieve your swollen eyes or puffy eyes, not dark circles. However,I recommend that you could try to put some lemon slices to your eyes or potato slices. More importantly, a good rest and healthy diet is the key to healthy eyes.
Yes, a lot of people use such way to get rid of the dark circles around the eyes. You could put the spoon one side to cover on the eyeballs surface. Your blood circulation around the eyes will move fast. You could find that your continuous doing this will make your dark circles around the eyes get released.