Sure.If you wear sunglasses on top of your contact lenses, the sunglasses will protect your eyes from harmful sun rays. Additionally, the sunglasses can also prevent the wind and sand getting into your eyes in case your eyes get infected when you wear the contacts.
Do your contacts and sunglasses both have prescriptions? If you wear a pair of prescription contacts and put on a pair of prescription sunglasses at the same time. They are not good for your eyes. You may suffer from headaches or even vomit because the total degrees are not suitable for your eyes.
Why not buy a pair of prescription sunglasses? If you have some vision problems, prescription sunglasses can help correct your vision problem as well as block harmful UV rays for your eyes. If they are polarized sunglasses, they can filter glare. Hope this helped!
If your contacts have prescription while your sunglasses are a pair of plano sunglasses, they can be put on together. The contacts can help correct vision problem and sunglasses can block UV rays and filter glare for your eyes. Both of them are good for your eyes. But if both of them have prescriptions, you'd better not wear them together. Hope this helped!