Not according to the TV show but I've heard that idea before. It's an interesting twist to the show. I've also heard of people saying that Franny from foster's home was simply an imaginary friend of the older lady. I think people like to try to give TV shows a twisted ending for the fun of it.
I think Tigger would've immediately pointed out his schizophrenia in the show, and then another movie would've been made, talking about how they went on an adventure with the psychologist in the Hundred Acre Wood.