Can rust cause a car to age?

To answer this question precisely would necessitate me knowing what you mean by the Word "age". If car A is 10 years old with no rust, but car B is 10 years old with rust, they are both 10 years old. The age of both cars is 10 years. Only time itself causes age.

However, if you ask the question "Can rust cause my car to become no longer useful?" The answer to this is - yes. Rust eats away critical parts of the car so that it is no longer safe to use.