Nope
Joker's hand in the sixth panel, which would be when the Joker is beginning to get choked in the 'Batman kills Joker' fiction shows the Joker's hand relaxed. Not clenched, not reaching up to his own neck, just conversationally extended.
The seventh panel shows the Joker and Batman's feet planted on the ground. The Joker's feet aren't lifted, the aren't apart. They are relaxed, on the ground.
The idea that Batman strangles or snaps the Joker's neck has no basis in what you are actually shown in the panels. Batman places a hand on the Joker mid-laughter, but there's no evidence he does more than that.