Thanks a lot, System_D.
I think I will listen to someone who served on a dozen of SC and follow the norms!
I really appreciate your input, and those of others. You reply indeed answered my question: there might be a negative effect if I contact them now. So I will wait, and let you guys know in the end if I get the onsite invitation after all.
Filmcam, I've been on almost a dozen search committees, and I want to let you know that you're thinking about search committees and rankings in the wrong way.
When an applicant does things that are outside of the norms and expectations of an academic search, like contacting the search committee, it makes the applicant look like s/he was not well-socialized into those norms. No one wants to work with someone who doesn't know how to "act right."
So yes, contacting a search committee at an inappropriate time or for an inappropriate reason can definitely jeopardize one's candidacy. But it's not a numbers game. It's a "feeling" game, as in "something about this applicant doesn't feel right."
When it comes down to it, Filmcam, search committees are looking to hire someone they believe can achieve tenure at their institution, but they are also looking for someone they believe they can work with. That elusive quality is often called "fit," and truly means "fitting in." Think about that.