He can, yes. In Death of the Family arc, he caught Batman and had him in an electric chair in one situation and in another had him and all of the other members of the Bat-Family tied up. He has had so many chances to kill Batman, but passes up on it, because he loves the company.
The Joker has been determined to kill Batman more often than not, certain writers have it where he isn't willing to kill him those moments simply stand out more.
There have been a lot of moments where he is going to be thrown into acid/fire pit or dodge a bullet from his gun.