Jackie chan is an actor. He spent many years training in the opera that while physical didn't teach him much more than the basics of some martial arts. Jackie chan holds no Black belts and has little experience fighting outside of his movies. He spend much of his time donating to charity and directing different projects/pursuing his musical career. Jackie chan has more experience than the average person but would most likely lose in a match (sparring or mma style) to a medium rank acolyte of most martial arts.

Anyone can fight in real life, howbeit with varying degrees of skill.

Contemporary Wushu might not teach self defense at face value, but the technique are still there, even if exaggerated on, and self defense logic isn't hard to deduce. The only difference maker is how you go about training after such a point.

He was trained in the Beijing Opera and not in formal martial arts, but that being said, the training was stricter and tougher than almost any martial art school nowadays, so he has training on his side, plus I'm sure he's had to learn a lot of techniques for his movies so I wouldn't be surprised at all if he was a competent fighter.