How exactly does submitting an interdisciplinary NSF fellowship proposal affect your chances at winning it?
According to the NFS


  Your application will be assigned to the field of study you list first
  in the Proposed Graduate Program section. ...
  Therefore, you should choose which field you list first carefully,
  with consideration of which panel has the most appropriate component
  fields. ... All interdisciplinary applications are clearly marked as such during
  the review process. Many panelists have interdisciplinary expertise
  and are capable of evaluating interdisciplinary applications.
  Additionally, if necessary, the panel can transfer your application to
  another panel for either a full review or for commentary and feedback.


While in some cases they might average the scores, this does not appear to be a requirement. I would suspect that in most cases they would do the review within a single panel and rate you accordingly and only seek expertise outside the panel if absolutely necessary.