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.