Do Winnie the Pooh Characters really represent different mental disorders?

Long after my time.

I think it depends on who you ask, and from whose perspective. From a child's perspective, particularly one whose innocence is still whole, there is nothing necessarily wrong with any character, and each of them learn something in each story.

From an adult's perspective I think it is a risky measure to actively look for anything internally wrong with anyone, including fictitious characters, at least until some quality in-depth investigating has happened. The quacks, as I've come to think of them, who dictate certain psychological doctrine have spent so much time finding something flawed in everyone that they completely and utterly failed at defining what can be considered as both normal and reasonable of an average person. If the author wrote these as a means of coping with his own trauma, then that's that. End of story, and I've come to mildly despise people who have us look far deeper into a character or a story's circumstance than the author ever intended. JRR Tolkien's Middle Earth is rife with such examples. I'm not saying he gave us shallow writing; far from that, but some things are left mysterious on purpose from the author's perspective.

A comprehensive psych eval of all of the characters in the Flintstones would certainly be interesting