From my experience, the AWA score will hardly have any impact at all. Please remember that PhD applications are evaluated by faculty versus MBA applications, which are judged by admission commitees (who do only that for living!). Professors rarely know all the details about the scoring procedure and they don't care too much.
As a rough guideline, in the schools you target, the members of faculty who have been "selected" to do PhD admission will read all the applications with a GMAT score starting with 7. If you are in this group, your admission really hinges mostly on your recommendations and your statement of purpose.
Given that the admission rate for PhD programs is often only one percent, it is a good idea to write 10 or more applications. Just be careful to tailor the statement of purpose towards each school, so it really matches with interests of the faculty there. When you read some applications it is quite amazing that the applicant did not do enough research to find out that nobody would be able to advise his proposed topic.
Joern Meissner, PhD
Lecturer in Management Science, Lancaster University Management School
Research Homepage: http://www.meiss.com
Academic Director, Manhattan Review GMAT Prep