Yes, it can help reduce dark circles to some degree as the moisturizer can clean the skin of ocular region and has an effect of elimination of toxicant and moisture and nourishment, hence helping reduce dark circles. As a matter of fact, there are many other methods helping reducing dark circles. You can pour the boiling water into the washbasin for steaming your face for two or three minutes, and then apply chilly compress onto the eyes. Massage has an effect of relieving dark circles, too. Besides, you should balance your diets and eat more fruits with vitamin C and do appropriate aerobic exercises to promote blood circulation, in this way, it helps reduce the chance of the formation of black circles. Also, sufficient sleep is necessary.
Actually, the moisturizer will make your dark circles get release for a while, not the basic cure. As we know, the black circles are caused by the lack of sleep, body disorder in work and so on. If you want to reduce it, you'd better get through the good sleep or the good habit of eating. That is the main and basic way to help you reduce the dark circles under the eyes.
It seems to me that you are going to turn to moisturizer for help. However, as a matter of fact, the function of it is not set out to relieve dark circles under eyes, but help to keep your face moist and nice. Therefore, you need to get some cosmetic products designed to tackle this problem. Also, you should keep a healthy lifestyle, which could permanently help you.