Somewhere in the SR4A books I believe it says baseball is one of the sports that don't allow Awakened, augmented, or Metahuman players. Seems awfully ignorant to me, and I'm a huge proponent of "the rule of cool", so feel free to hand waive that if it gets in the way of your fun at the table.
It's been a long time, so I may have some of this mixed up, but there was a novel waaaay back in the SR2 era about a wolf shaman that played baseball (as a professional or as part of a mission, I don't recall). The MLB used Awakened umpires to see if any of the players were using mojo to cheat.
As for Slugger himself, he looks legit, and I really like his birth name, nickname, and fake SIN name =] Personally, I'd remove Astral Perception and Eidetic Memory, as those aren't really Powers associated with The Adept Way of the Athlete, but it's your toon and you may have some good reasons for having them that I'm not aware of. All in all, that looks like a fun character to play.