Well, yes, in some degree, sleeping can do a good job to your pink eyes. As we know that it is an inflammation of the conjunctiva, and it occurs, when the tissue lines the inside of the eyelid. Generally speaking, pink eyes can be caused by some virus, bacteria. When it occurs, your eyes will be red, itchy, and even bloodshot. In some cases, being around a person who has conjunctivitis and wearing contact lenses may increase your risk of getting conjunctivitis. In my opinion, have a good sleep can be helpful for your pink eyes. Also, you need to take some eye drops.