You would need a plugin for that unless you can manually create it. Otherwise it will only upload to folders WordPress creates or one that you chose in the Media Settings. However, you can setup separate folders to put your media into and attach them accordingly but you wouldn’t be able to use the Media Uploader for that.
Actually I’ll just use the default media upload. I just have it upload the media files into the theme directory instead, since this is what I’m most likely to back up all the time.
Then I just put in the description of what the picture is about, like header, people, pets, etc.
Then I’ll just use the search if needed method if needed.