No, it's wrong. The article applies to the entire noun phrase. "A" is correct
If you say "an privacy" it'll sound like English isn't your first language.
If you say "an privacy" it'll sound like English isn't your first language.
Also, it's not even the noun phrase according to the sources I'm looking at (namely Merriam-Webster) which state that it is always dependent on the word directly following the article, not even the entire phrase.