You could try checking the browser history and form history. You may be able to see what e-mail clients are being used on the computer and even what screen names. You would not be able to do much more than snoop without doing anything illegal, unfortunately.
It is hard to know if someone has a secret email address since it is a secret in the first place. You can try to investigate by asking your friends, family and people you're close with if the person has a secret email address.