It was possible to activate Siri by using a long press on the headset remote, but when I try it on my 5S/7.0.4 it's not working any more. There is no setting to enable this either.
I just tested it and it seems Siri will only activate if the phone is unlocked, if it is locked I can only start/stop music.
(there is a two year old post with a similar problem: https://discussions.apple.com/message/16692414)