Far from it.  As a changeling, Buzz Buzz is capable of using magic, and there is no difference between a unicorn’s magic and a changeling’s magic (save shapeshifting which comes naturally to changelings) so he could use unicorn magic.  However, transmogrification requires intense concentration and a LOT of magic.  

Changelings have comparatively small magical fonts, they don’t have much magical energy to work with, and Buzz Buzz has no concentration whatsoever.