All public boards on Chartmat are by default indexable from Google and other search engines. This means that if you make your board public, it could show up on Google.
If you do want to make it private, you can easily add a "noindex" meta tag. Simply switch it on in the board settings.
You can read more about the noindex tag here.
Keep in mind that your board will still be public and can still be viewed by anyone with the link. If your board contains sensitive data don't make it public!