Why would the tension screw on a Brooks saddle have unscrewed to zero? What negative effects?
Checking the tension on a Brooks saddle is part of the regular maintainance. Any bolt that doesn't have sufficient tension on it will move due to random road vibration. 

From 

http://www.brooksengland.com/getting-in-touch/faqs/saddle_maintenance/


  Q: Why have the Rails / Tension Pin / Backplate on my Brooks saddle
  broken? By far the most common cause of breakages of the Rail,
  Backplate and Tension Pin is insufficient leather tension. Brooks
  recommend a routine six-monthly check of the tension, and adjustment
  where required.


A bolt stays in place due to the friction applied to the threads by the tension in the bolt. In effect you are "stretching" the bolt so it constantly pulls on the threads
to create the friction to hold the bolt in place. In the Brooks saddle case the force
is actually a compression, but the principal is the same. 

As long as you put the tension back and check it on a regular basis, I don't think there should be any long term damage to the saddle.