In addition to what Jeffro mentioned, if you search they won't know but if you click on their profile it might show that. I'm not really on facebook (I have an old fake account that I never log into) but other social sites i'm on do that. You can always try searching without logging in but facebook isn't too keen on that and usually hides most information.
Also if you let them have access to your email address book you may get some "interesting" suggestions. Pretty much any information you put in will be used to make recommendations. Schools, jobs, where you lived friends of friends, etc...