He's a tech geek. Why wouldn't he have known about transporter tech as a teen? Those are the formative years.I don't think so, more than once on the show it's been said that there a steep selection process to gain entry into Starfleet, it's just plain hard to get in.
In addition, Barclay said that his fear of the transporter was based upon his detailed knowledge of it, would he have possessed that detailed knowledge as a older teenager prior to entering Starfleet and going through Starfleet technical training?
Honestly, I have no problem expecting that the Starfleet who let's a blind guy with artificial vision into their ranks might also let a guy with some emotional discrepancies. They got Vulcans in Starfleet. Clearly, odd emotional conditions are not a big worry for them