I do not think so. Dark circles is caused by melanin accumulated around your eyes,which is the waste left by your blood run by there. Rather than using cold spoons, you should use hot pack. I have some advice for you:
First tip: you can rub you pulms several times and cover them on your eyes at once,and with the heat,try to turn your eye balls around for several rounds. Repeat it for times whenever you are unoccupied. It can help improve your blood circulation so that the letout of eye wastes can speed up.
Second tip: choose fresh potato and chop it into thick chips and cover them on your eyes for 15 minuets everyday before sleeping. It is very magic whatever you believe it or not.
Hope that will help.
Well, sounds like that you are gonna treat your dark circles, for they really pissed you off right? Anyway, I should remind you that cold spoons simply have little connections with dark circles, for those stuff are primarily caused by a lack of vitamins, poor rest and some other diseases inside your body. Thus, you gotta pay attention to those aspects instead of focusing on some special and strange ways. Hope you find this useful.
If you want to reduce your dark circles around the eyes which is caused by the lack of sleep, bad blood circulation and so on, you could use the warm compress instead of the cold spoons. The warm compress home remedy could increase your blood circulation at the whole body. You should not stay up late at night which will make the dark circles get serious.