Yes. However, your CMS of choice should give you the option of allowing the search engines to index your pages. For instance, wordPress give you the option of allowing, or not allowing Search Engines to index your site, but they warn that the Search Engine may, or may not, honor your request.
Bottom line, if there is something sensitive in a post, that you don't want to see on page 1 of Google, don't publish it.
The little image there is from a typical "Privacy Settings" page in a WordPress dashboard