You can go their profile page and add them there.
http://www.chess.com/members/view/username
Hopefully they can decline the invitation ?
Yes, it can be declined, accepted or ignored. If you decline, the site wants you to fill out why. I don't know if that gets sent or if it allows you not to put in anything. If you just do nothing (ignore) it just stays in your Friend Request section.
On the drop down menu it only lists an email invite method.