Here's what happens if you're not on the list: http://i.imgur.com/zfHp1.png
There's nothing more at the end of the page. Basically they try to get you to use one of their password managers. There is no way to tell if this site is storing your emails, but I was ok with doing it with my secondary email because you don't have to give your password.
There are two potentially malicious things that a site like this could do with an email alone: add you to a target list, or add you to a spam list. I'll see if I start getting any spam, but doubt that I will because I think that a site this big is probably legit (or smart enough to make it seem as though they are*) and like to think that spam filters are sophisticated enough to block random messages (unlike my phone which keeps getting calls for a free cruise).
Ultimately, I agree completely with @xce, and think that changing your password regularly is the best bet. When it comes to your email address, I would be more concerned about password strength or simply a server side vulnerability (like what happened with Yahoo) then anything else. Usually in either case you'll be aware, as the hacker wants to do something with your email. If you're completely worried that you're already hacked by a passive hacker, switch to a new email address, make a much stronger password and switch all of your email addresses diligently. This is typically more work than it's worth, in my opinion. Unless you work for the Government maybe.
Edit: *added necessary skepticism