If you have a new computer, and a new chrome/gmail account and have never visited a website before, then go to CB, create an account, will you see ads?

Of course.

Ads can target you based on search history and sites you have visited but that isn't the only method. It's not always that laser targeted. Also, that method of targeting is under lots of scrutiny and is becoming harder and harder to do.

Ads are often targeting people based on other factors such as demographics, geographics, and some are even much more broad.