I always thought Barclay was one of the dumbest characters in Trek. Granted he's a capable engineer, but someone with that many obvious mental health issues should never be allowed aboard a starship. He's unstable to say the least and I wouldn't trust him with my car...if I had a car. How he ever made it through the academy and manged to get posted on the Enterprise-D is miraculous. He must have had dirt on Picard...scandalous photos of his vacation on Risa no doubt. That just about he only way to justify how someone so unstable would be allowed serving in Starfleet, which constitutes a character so poorly created that he is in fact, dumber than Tuvix.
That being said, I've only seen Tuvix once, and only remember the general premise of the episode, so far in as the two main characters being fused into one new being. Certainly stranger things have happened with the Transporter, so it's not so far beyond the realm of possibility that in of itself, the creation of Tuvix is inherently a poor idea.