Is it possible to use an image in my themes directory as the default image of an image field? This question addresses how to add an image using a URL rather than a direct upload using the filefield sources module.  However, that module does not allow the "Default image" to be set.

For my image field, I want users to only be able to upload files (just the way Drupal comes by default).  However, I want the default image to be stored in my themes directory if possible in order to ease deployment across multiple sites.  Is there a way to set the default image to an image on the server rather than having to upload it?

I'm using Drupal 7.
You could make a module whose sole purpose in life is to copy an image into the appropriate place in the file system. Then it would be in code and versionable, independent of what you did with the theme.