As an owner of a ced 7000 I wanted to know so I grabbed a pair of headphones and tried.
In summary, it does work with headphones which is a game changer for me! My wife also would get annoyed by the beep so I only use a timer when she isn't there.
You can turn off the external beep by going to the "silent op" setting and selecting "on". It emits more of a click than a beep through the headphones but it seems like it will work!