Neither is Vertigo.
I dunno, don't you think it's a really weird fit?
I think Constantine's lack of decent combat/magic abilities and reliance on wit, subtlety, trickery and his reputation as a complete bastard is kinda fundamental to the character. It's where I feel the new DC version (too much magic), the TV show (too much chanting), and the film (too much Holy Shotgun) fell flat. That's beside the point, of course. It'd just be nice for Hellblazer to be translated to another medium and actually work/be appropriate for once.