No. I don't believe he does. He can pay attention when he feels like it, just like Garp. But most of the time, he just isn't interested and does something else. It's not like anything actually distracts him from paying attention.
I honestly never thought about that but if I were to guess I would say he definitely has ADHD. He is impulsive in his action against other people, doesn’t listen to what his crew tells him. He also switches between thinking about food, meat and becoming the pirate king. Plus all that jumping around and acting jittery is an everyday business.
