Yes, it is very possible and I alway get this kind of symptom too when I catch a cold. Possible causes of goopy eyes include heat accumulated in body or eye infection. Actually gum in eyes is very normal. Glands in eyelids secrete oil to lubricate our eyes. During our sleeping, the oil keeps our eyes shut to avoid excessive tear evaporation. When we wake up in the morning, we can find gum in eyes, which is actually the oil mixed with dusts got into eyes in daytime. If people are healthy, then gum in eyes is moderate. Once you find increased gum in eyes in a sudden, which might be a signal of eye infection. A cold is upper respiratory infection disease. It is very possible to spread the virus to eyes, resulted in eye infection. So it is common to have goopy eyes from a cold. I suggest you to wash your eyes with saline water and instill some chloramphenicol eye drops. You can also drink some detoxification tea to help remove the heat and toxin accumulated in your body. After drinking the tea, use the cold tea bag as compress.
It is true that cold can cause goopy eyes. Goop eyes are always noticeable because of redness in eyes and swelling on eyes. This may possible due to bacteria and virtues infection. Cold is one of diseases which produces bacteria and spreads them. Bacteria and virtue can get into your eyes through tear duct, and then you may easily suffer goopy eyes. It's easy to be found that your eyes are redness and swollen. A viral infection such as that caused by the common cold virus does not typically require treatment. The infection and resulting symptoms will clear within a few days or as the virus resolves. However, if you get severe cold, then medicines must be taken and clean up your hands before eat anything. Please keep in mind that do not rub your eyes with hands, or bacteria can enter your eyes. Take easy. Goopy eyes are not serious and you'll be fine in a week unless you take good care of yourself.