"Radio personality" is like anything- a combination of your own personality and the skill you develop, which presents as your style. I think it's quite like most activities, including programming. Some people have the capacity to handle the technical aspects, but their code is nothing you'd want to spend time trying to understand. Some people are great at documenting their code, but they never bother doing much of interest...

From my experience as a DJ (currently @ WESU, Middletown), a lot of the skills are acquirable- feeling comfortable on mic, controlling your quality ("ummm", "uhh", etc), knowing how to segue, and all the technical operations using the equipment. It takes dedication to learn them, but no atypical capacity for learning is required.

However, some people just have more listenable voices, or a quality of speaking that's more appealing to listen to. There's a subjective element provided by the listener / user that will vary from case to case.