http://www.youtube.com/watch?v=2bOJ3uR0s2s
New batman would never be seen doing something like this.
What, like Nolan's Batman? I could see him doing that, actually. He already had his whole conflict of "I should kill the Joker, but no killing is wrong I won't do it, justicccceee." I could see him doing something similar.
Frank Miller's Batman might not. Joel Schumacher's Batman wouldn't even have this kind of deep emotional story to begin with. Tim Burton's Batman I can see that happening, and Micheal Keaton would be perfect doing that. Adam West's Batman would do it if he were in the situation, but then again, I don't think his Batman ever saw anything that deeply rooted, his stories were about action and comedy, not human nature.
I could say that the "new" Batman, assuming we're speaking in film, would do it. The Batman of Arkham City would for sure do that because he's Kevin Conroy and, if I'm not mistake, the same Batman from the animated series (and subsequently all of the spin offs, Justice League, Beyond, etc) continued.
The only Batman who flat out would not do it is Batman: Year One's Batman or The Dark Knight Returns' Batman.