I've been aware of that button for years (it was also in RTW1), yet I have never pushed it. Does anything unusual happen when you issue a disengage order (other than, you know, disengaging)? For instance, do ships that are within range of the enemy stop firing? Do ships under player control disregard player-issued orders and turn away from the enemy? What happens if you issue a disengage order and then change your mind? Can you toggle off the order with the same button?
I guess I should just push that button sometime.
The disengage button will make all AI controlled divisions, including any support force, try to increase range or disengage.