I think combat should be fairly regular, but shouldn't overwhelm the storytelling capacity of this campaign. I'd say the ration would be, what, 60:40, RP to combat? I'm not sure how that really translates. Technically, I guess it might even lean closer to 70:30, given how little space combat might take up comparatively.
As far as tone, I always thought Sharn was primarily best for pulp-noir, but pulp-occult works really well too. I don't mind genre-crossing, as a story such as this would likely involve quite a few. Definitely plenty of drama, and of course with the trauma and evil machinations of the situation, a touch of horror/thriller is expected as well.