I'm doing some research around the same issue more or less. My understanding is there's a big difference between digital and analog servos in this regard. When an analog servo stops getting signals it stops trying to do anything. A digital servo (from what Hitec support told me) will continue to hold its last position, unless failsafe is set to "on" in which case it will hold its failsafe position. Also from reading, digital servos do continue to draw power even when they're "idling", which I interpret to mean in position with no force acting on it, but it's a low current draw relative to when the motor is doing work.
My question from another concurrent post is, does the "detach" command actually cut power to the servo. In thinking about it, the servo is in all likelihood drawing power from an external source therefore the answer would be no. Meaning in the case of a digital servo run from an Arduino, "detach" would not necessarily cause the servo to let loose of its grip. I'm looking for a definitive answer about this because in my application it seems like the servo does let go, but then sometimes it doesn't. I don't know definitively what the behavior should be i.e. does the servo know what "detach" means? Or does the servo just see that it's no longer receiving a signal...