I tend to keep things in an orderly fashion and I defrag before system shutdown. Does this negatively impact the chances of recovering files?
Yes. A defrag may overwrite the space that deleted files occupy.
I believe defragging at shutdown is overkill.
In context of this thread, recovering files, if you're concerned about data loss - just be sure you've got backups of the important stuff. That way, you won't have need for recovery programs.