The main purpose of a swim cap is to make you faster and have less of a drag in the water, not to protect your hair from chlorine damage. Many people with long hair have trouble with it dragging them down, getting in their face or making it impossible to hold the head at the correct positions. A swim cap can help these problems.
In the past, swim caps were usually made of rubber or material. The hair would still become saturated with water. So these types of caps would have no effect on keeping the hair from becoming damaged by the chlorine and chemically treated water.
Today, there are swim caps available in latex and silicone that if worn properly can keep the hair dry. It is my understanding that it's hard to get that perfect fit and you should opt for a higher quality one for this reason. Some people say that you have to wet your hair beforehand in the shower to get the cap to fit correctly, while others say that you can just braid and tuck it under the hat.
The article I found goes into great details about all of this. Long story short, if you can find one that will allow you to keep your hair dry, it should help. blog.swimator.com/2010/11/should-i-wear-....
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