Yes, you can wear the eye patch on the precondition that the eye patch is clean with no bacterium which will make your pink eyes get serious. But I suggest you not to wear it because the contagious character of the pink eyes. You will leave the bacterium in the patch which will not be used after your eyes get well.
No, you had better not to do that. Pink eye or conjunctivitis is one of the most common eye problems, but it can be contagious easily due to the invisible bacteria or virus. The eye patch is used for you to hidden lights into eyes, that is to say, it need to be placed over your eye area and touch eyes directly. When you get pink eye, it usually occurs only in one eye initially. When the eye patch touches the pink eye, the bacteria or virus would pass to the eye patch, and then cause the other eye to be pink eye. On the other side, you should provide relax and breathe freely environment is better for treating the pink eye.
You should avoid wearing eye patch if you got pink eyes. Pink eyes is an acute infectious eye inflammation. If you wear eye patch, the temperature of the eyes would become higher and breeding much bacteria. The best way is to keep cool, and avoid using any kind of oculentum, thus can prevent eye temperature from increasing.