I have signature display on both because I enjoy the interesting ones (I find the ones with computer specs rather dull) and because I'm part of the Dreaded Signature Police, making sure that they stay without the size limits described in the forum rules.
Perhaps people turn invisible mode on because they want to visit the forums without getting contacted by other members who see them online, but if that was the case I'm not sure why they'd have receipt of email and/or Private Messages enabled in the User Options in the first place.
On a related topic, I don't understand why many members have the "Receive Email Notification of New Private Messages" option turned off. Do they get so many messages that they'd be overwhelmed if they got email about each one? Do they check for Private Messages so often that they don't need to be notified? As things stand, some people reply a month after someone sent them a Private Message and say "sorry, I didn't notice your message".