Would he fit in with the whole story?

Depends on the story. With the announced reboot where they are supposed to make a more JLA friendly batman, it would likely be hit or miss.

No, a cartoon yes, but I would much rather see, Poison Ivy, Mr. Freeze, The Riddler, Hush, Harley Quinn or the Penguin be portrayed in a new Batman movie.

That much is true, there are a slew of Batman villains that should get a movie before Deadshot

As much as I love Deadshot, I would never really be interested in Deadshot in a Batman movie. Deadshot never has some big master plan, his skills in unarmed combat are mild (at best) compared to Batman. Considering his only strength is his guns, it just wouldn't make for a compelling movie. I would, however, love to see him as a villain in another character's movie. This will never happen, but I'd totally freak if there were a secret six movie.

I think he'd make a great side-villain, sorta like Bullseye's role in Daredevil. Underrated movie BTW.