That certainly is one way they can die. In captivity, rattlesnakes have an average lifespan of over 20 years, but that is significantly lower in the wild. There are a lot of ways fo a snake to die in the wild, and while age is not the most prevalent, it is sure an option. 

I suppose any animal could die of old age if given the chance. Rattle snakes can live for nearly 25 years, but rarely do so because of other incidences. They may become prey for some animal, really anything can happen.