Warm is certainly always better, but given how opaque ATS processing is and the number of submissions they get, I'm not sure that you're worsening your chances by taking a shot at direct. Look at it this way - if the manager just deletes it as spam but HR screens it in, they'll see it, or vice versa. And if the manager opens it, I don't know many people that would can a resume from a qualified candidate because it came direct. While ATS'es and HR screening are seen as huge obstacles from the outside, on the inside we're pretty happy to get a qualified candidate by any means. And if the candidate isn't qualified, no harm either way.