Ok, your question is really fun. And as a matter of fact, the primary reason why so many people choose to go out with a pair of sunglasses is to protect their eyes from getting burned by the sun. And sometimes a small amount of people do this due to looks reason, they want to be cool and stay mysterious. Your assumption may not be right. Just try to get a pair of sunglasses to get rid of the burning sunshine.
Yes, the sunglasses could make the skin around the eyes less tan because of the sunshine. It is the special coating part of the sunglasses that help your skin around the eyes prevent from the uv rays and other bad sun lights. It is very necessary for you to wear the sunglasses in the strong sun light. It could protect your eyes.
Sunglasses can protect your eyes and facial skin from ultraviolet which is really harmful to both your vision and your skin.
With the sunglasses as a shielded from the sunlight, the part which is hidden under sunglasses has less assess and exposure to sunlight. Therefore, it look less tan or paler than other parts on the face.