I've seen "functionary" before, Silver. I'm not sure I've ever seen "public functionary", however. I'd say that "public servant" or "public employee" would be easier to understand. So would "bureaucrat", especially if you want the reference to sound slightly insulting.
And also, I tend to associate the word "functionary" with someone who is not necessarily a public servant (may be a party functionary) but is a high-ranking figure, possibly a well-known one. A functionary, for me, is more of a political figure.