Of course smaller firms care about that stuff. Why would they not? They're a potential employer, and they would like to try to hire the most qualified candidates they can.
And I think that if you really want to teach, you shoudl try to transfer into the highest ranked school you can get to. Yes, it may not be absolutely necessary, since once you get 10-15 years experience, author some articles, etc., you might be able to get a job teaching no matter where you go, the fact remains that being a law professor can be just as prestigious as BIGLAW.
I think that if you look at bios for many, many schools, I think the T1 schools will be much more heavily represented than any other tier. While it may not be true, there seems to be a lot of emphasis on the generalization that the higher ranked schools seem to be more focused on the philosophy and doctrine of the law, and not as much on the practice of law. I'm not saying these generalizations are always true about all schools, but it's hard to argue that it's NOT true. This may be part of the bias toward the T14's heavy representation in the academic community.