Not exactly.
Urianger is only using thou/you incorrectly if you assume he's doing it to sound formal. It would probably be more accurate to say that players incorrectly think he is talking formally because he uses "thou".
He does use "you" occasionally in formal situations, such as addressing Feo Ul as "Your Majesty".
Also, it's not just a matter of thou being informal and you (or ye) being formal. They originated as single and plural forms, and only later the plural "you" picked up its second role as a formal singular pronoun (and eventually took over as the only one in general use).
https://en.wikipedia.org/wiki/Thou
https://en.wikipedia.org/wiki/Ye_(pronoun)