Offhand I know of little internally which cares about the post_parent on an attachment except the post admin and rewrite (permalink) rules.
Images/files show under Browse for the post they're attached to instead of Browse All, so there's a bit of organization value to it.
With rewrite rules when using anything other than the default permalink you can do this:
Post:
http://guff.szub.net/2006/01/29/woof
Attachment:
http://guff.szub.net/2006/01/29/woof/fire-dog
Though at this point I'm not sure how useful it is. :)
As for the rest, an image correctly linked to in a post should display. If the directory structure remains the same (i.e. wp-content/uploads or whatever), moving your blog up a directory should not affect the internal stuff on the attachment, but the link or image reference to it in a post will be affected if your image director(y|ies) move along with it. This would be the case with or without an "attachment" feature.